Question

the width of a rectangle is 5 cm and its diagonal is 13 cm what is its perimeter?

Answer 1

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BE BRAINLY

Answer 2

Length = x.
Breadth = 5 cm.
Diagonal = 13 cm.

We know that a diagonal divides a rectangle into 2 right angle triangles.

According to Pythagorean theorem:

In a right angle triangle,

$hypotenuse { }^{2} \: = \: adjacent \: side {}^{2} + opposite \: side {}^{2}$

So,

$13 {}^{2} = 5 {}^{2} + x {}^{2} \\ 169 = 25 + x {}^{2} \\ 169 - 25 = x {}^{2} \\ 144 = x {}^{2} \\ \sqrt{144} = x \\ x = 12 \: cm$
So, we found the length of the rectangle that is 12 cm.

Now,
perimeter of a rectangle = 2(length+breadth).
= 2(12+5).
=2(17).
=34 cm.

Therefore, the perimeter of the rectangle is 34 cm.