Question

The perimeter of square A is 5 times greater than the perimeter of square B. How many times greater is the area of square A than the area of square B?

Answer 1

If the length of each side of a square is `z` then its perimeter `P` is given by:

`P=4z`

Let the length of each side of square `A` be `x` and let `P` denote its perimeter. .
Let the length of each side of square `B` be `y` and let `P'` denote its perimeter.

`implies P=4x and P'=4y`

Given that: `P=5P'`

`implies 4x=5*4y`
`implies x=5y`
`implies y=x/5`

Hence, the length of each side of square `B` is `x/5`.

If the length of each side of a square is `z` then its perimeter `A` is given by:
`A=z^2`

Here the length of square `A` is `x`
and the length of square `B` is `x/5`

Let `A_1` denote the area of square `A` and `A_2` denote the area of square `B`.

`implies A_1=x^2 and A_2=(x/5)^2^`

`implies A_1=x^2 and A_2=x^2/25`

Divide `A_1` by `A_2`

`implies A_1/A_2=x^2/(x^2/25)`

`implies A_1/A_2=25`

`implies A_1=25A_2`

This shows that the area of square `A` is `25` times greater than the area of square `B`.