Question

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.

Answer 1

2 steps to this problem.

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

2L + 2W

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

2L + 2($\frac{3}{4}$)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. 

$a^{2} + b^{2} = c^{2}$
--> 
$20^{2} + 15^{2} = c^{2}$
--> 
$\sqrt{20^{2} + 15^{2}}$ = diagonal length = 25