Question

The width of a recangle is 5 cm and its diahonal is 13 cm. What is its perimeter?

Answer 1

Width = 5 cm.
Diagonal = 13 cm.

We know that, a diagonal divides a rectangle into 2 congruent triangles.

According to Pythagorean theorem in a right angle the hypotenuse² = adjacent side² + opposite side².

Here our hypotenuse is the diagonal and adjacent side is the width. Let the opposite side that is length be x cm.

So,

13² = 5²+x².
169 = 25+ x².
169-25 = x².
144 = x².
√144 = x.
12 = x.
x = 12 cm.

Now,

Perimeter of the rectangle:

=2(length+width).
=2(12+5) cm.
=2(17) cm.
= 34 cm.