Question

A piece of cardboard has been cut into a rectangle with side lengths represented by 9.5x+14.3y cm and 11.7x+22.8y cm. What is the perimeter of the cardboard in terms of and ?

Answer 1

Given:

Sides of a rectangle are 9.5x+14.3y cm and 11.7x+22.8y cm.

To find:

The perimeter of the cardboard in terms of x and y.

Solution:

We know that, perimeter of a rectangle is

$Perimeter=2(length +width)$

Now,

$Perimeter=2[(9.5x+14.3y) +(11.7x+22.8y)]$

On combining like terms, we get

$Perimeter=2[(9.5x+11.7x) +(14.3y+22.8y)]$

$Perimeter=2[21.2x +37.1y]$

using distributive property, we get

$Perimeter=2(21.2x) +2(37.1y)$

$Perimeter=42.4x+74.2y$

Therefore, the perimeter of the cardboard in terms of x and y is 42.4x+74.2y cm.