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the perimeter of a rectangle is 70 inches. the ratio of the length to width is 4:3. find the length of the diagonal of the rectangle.

Sagot :

2 steps to this problem.

1) Figure out the length of the sides. The perimeter is:

2L + 2W

We know that the width is [tex]\frac{3}{4} [/tex] of the length, so we can rewrite this to be 

2L + 2([tex]\frac{3}{4} [/tex])W

or in other words, 

3.5L = 70
-->
L = 20
--> 
W = 15

2. Figure out the length of the diagonal. The shape is a right triangle, so you can use the Pythagorean Theorem here. 

[tex] a^{2} + b^{2} = c^{2} [/tex]
--> 
[tex] 20^{2} + 15^{2} = c^{2} [/tex]
--> 
[tex] \sqrt{20^{2} + 15^{2}}[/tex] = diagonal length = 25
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