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.