Hypotenuse known , the ratio width : height known, How to find width and height value?

Clash Royale CLAN TAG#URR8PPP

up vote
2
down vote

favorite

Premises:

The nature of the problem is with respect to TV dimension.
I came across this when i was planing fo TV space required to mount onto my Wall.

Question:

How to find width and height of rectangle?

Known Value.

• the ratio of width to height is 16:9.


• the hypotenuse is 42 inch (106.68cm)

ratio rectangles

share|cite|improve this question

asked Jul 29 at 13:09

user219791

111

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Look up the Pythagorean Theroem
  – Jens
  Jul 29 at 13:33
  

  
  
  
  

add a comment | 

up vote
2
down vote

favorite

Premises:

The nature of the problem is with respect to TV dimension.
I came across this when i was planing fo TV space required to mount onto my Wall.

Question:

How to find width and height of rectangle?

Known Value.

• the ratio of width to height is 16:9.


• the hypotenuse is 42 inch (106.68cm)

ratio rectangles

share|cite|improve this question

asked Jul 29 at 13:09

user219791

111

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Look up the Pythagorean Theroem
  – Jens
  Jul 29 at 13:33
  

  
  
  
  

add a comment | 

up vote
2
down vote

favorite

up vote
2
down vote

favorite

Premises:

The nature of the problem is with respect to TV dimension.
I came across this when i was planing fo TV space required to mount onto my Wall.

Question:

How to find width and height of rectangle?

Known Value.

• the ratio of width to height is 16:9.


• the hypotenuse is 42 inch (106.68cm)

ratio rectangles

share|cite|improve this question

asked Jul 29 at 13:09

user219791

111

Premises:

The nature of the problem is with respect to TV dimension.
I came across this when i was planing fo TV space required to mount onto my Wall.

Question:

How to find width and height of rectangle?

Known Value.

• the ratio of width to height is 16:9.


• the hypotenuse is 42 inch (106.68cm)

ratio rectangles

share|cite|improve this question

asked Jul 29 at 13:09

user219791

111

share|cite|improve this question

share|cite|improve this question

asked Jul 29 at 13:09

user219791

111

asked Jul 29 at 13:09

user219791

111

asked Jul 29 at 13:09

user219791

111

111

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Look up the Pythagorean Theroem
  – Jens
  Jul 29 at 13:33
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Look up the Pythagorean Theroem
  – Jens
  Jul 29 at 13:33
  

  
  
  
  

Look up the Pythagorean Theroem
– Jens
Jul 29 at 13:33

Look up the Pythagorean Theroem
– Jens
Jul 29 at 13:33

add a comment | 

2 Answers
2

active

oldest

votes

up vote
1
down vote

It's simpler to solve it formally: let $H$ be the hypotenuse, $h,w$ the height and width, $r$ the ratio $w/h$. Just apply Pythagoras' theorem:
$$H^2=h^2+w^2= (1+r^2)h^2,enspacetextso quad h=frac Hsqrt1+r^2,quad w=frac Hhsqrt1+r^2.$$

share|cite|improve this answer

answered Jul 29 at 13:43

Bernard

110k635102

add a comment | 

up vote
0
down vote

Write $w=16k$, $h=9k$ to get $42^2=w^2+h^2=16^2 k^2+9^2 k^2=(256+81)k^2=337 k^2$. Then $k=frac42sqrt337$ and therefore $w=frac42sqrt33716$ and $h=frac42sqrt3379$.
Note that $frac42sqrt337approx 2.28$.

share|cite|improve this answer

answered Jul 29 at 13:49

Jens Schwaiger

1,092116

add a comment | 

Your Answer

StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

 

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2866059%2fhypotenuse-known-the-ratio-width-height-known-how-to-find-width-and-height%23new-answer', 'question_page');

);

Post as a guest

Name Email

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

It's simpler to solve it formally: let $H$ be the hypotenuse, $h,w$ the height and width, $r$ the ratio $w/h$. Just apply Pythagoras' theorem:
$$H^2=h^2+w^2= (1+r^2)h^2,enspacetextso quad h=frac Hsqrt1+r^2,quad w=frac Hhsqrt1+r^2.$$

share|cite|improve this answer

answered Jul 29 at 13:43

Bernard

110k635102

add a comment | 

up vote
1
down vote

It's simpler to solve it formally: let $H$ be the hypotenuse, $h,w$ the height and width, $r$ the ratio $w/h$. Just apply Pythagoras' theorem:
$$H^2=h^2+w^2= (1+r^2)h^2,enspacetextso quad h=frac Hsqrt1+r^2,quad w=frac Hhsqrt1+r^2.$$

share|cite|improve this answer

answered Jul 29 at 13:43

Bernard

110k635102

add a comment | 

up vote
1
down vote

up vote
1
down vote

It's simpler to solve it formally: let $H$ be the hypotenuse, $h,w$ the height and width, $r$ the ratio $w/h$. Just apply Pythagoras' theorem:
$$H^2=h^2+w^2= (1+r^2)h^2,enspacetextso quad h=frac Hsqrt1+r^2,quad w=frac Hhsqrt1+r^2.$$

share|cite|improve this answer

answered Jul 29 at 13:43

Bernard

110k635102

It's simpler to solve it formally: let $H$ be the hypotenuse, $h,w$ the height and width, $r$ the ratio $w/h$. Just apply Pythagoras' theorem:
$$H^2=h^2+w^2= (1+r^2)h^2,enspacetextso quad h=frac Hsqrt1+r^2,quad w=frac Hhsqrt1+r^2.$$

share|cite|improve this answer

answered Jul 29 at 13:43

Bernard

110k635102

share|cite|improve this answer

share|cite|improve this answer

answered Jul 29 at 13:43

Bernard

110k635102

answered Jul 29 at 13:43

Bernard

110k635102

answered Jul 29 at 13:43

Bernard

110k635102

110k635102

add a comment | 

add a comment | 

up vote
0
down vote

Write $w=16k$, $h=9k$ to get $42^2=w^2+h^2=16^2 k^2+9^2 k^2=(256+81)k^2=337 k^2$. Then $k=frac42sqrt337$ and therefore $w=frac42sqrt33716$ and $h=frac42sqrt3379$.
Note that $frac42sqrt337approx 2.28$.

share|cite|improve this answer

answered Jul 29 at 13:49

Jens Schwaiger

1,092116

add a comment | 

up vote
0
down vote

Write $w=16k$, $h=9k$ to get $42^2=w^2+h^2=16^2 k^2+9^2 k^2=(256+81)k^2=337 k^2$. Then $k=frac42sqrt337$ and therefore $w=frac42sqrt33716$ and $h=frac42sqrt3379$.
Note that $frac42sqrt337approx 2.28$.

share|cite|improve this answer

answered Jul 29 at 13:49

Jens Schwaiger

1,092116

add a comment | 

up vote
0
down vote

up vote
0
down vote

Write $w=16k$, $h=9k$ to get $42^2=w^2+h^2=16^2 k^2+9^2 k^2=(256+81)k^2=337 k^2$. Then $k=frac42sqrt337$ and therefore $w=frac42sqrt33716$ and $h=frac42sqrt3379$.
Note that $frac42sqrt337approx 2.28$.

share|cite|improve this answer

answered Jul 29 at 13:49

Jens Schwaiger

1,092116

Write $w=16k$, $h=9k$ to get $42^2=w^2+h^2=16^2 k^2+9^2 k^2=(256+81)k^2=337 k^2$. Then $k=frac42sqrt337$ and therefore $w=frac42sqrt33716$ and $h=frac42sqrt3379$.
Note that $frac42sqrt337approx 2.28$.

share|cite|improve this answer

answered Jul 29 at 13:49

Jens Schwaiger

1,092116

share|cite|improve this answer

share|cite|improve this answer

answered Jul 29 at 13:49

Jens Schwaiger

1,092116

answered Jul 29 at 13:49

Jens Schwaiger

1,092116

answered Jul 29 at 13:49

Jens Schwaiger

1,092116

1,092116

add a comment | 

add a comment | 

 

draft saved

draft discarded

 

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2866059%2fhypotenuse-known-the-ratio-width-height-known-how-to-find-width-and-height%23new-answer', 'question_page');

);

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Name Email

Name

Email

Name Email

Name

Email