Question

A 4 by 5 inch photo is enlarged by multiplying every

dimension by 2 to form a similar 8 by 10 inch photo. Find
the ratio of the perimeters and areas of the larger photo to
that of the smaller one.

Answer 1

Perimeter ratio = 2:1

Area ratio = 4:1

Explanation:

Perimeter

Perimeter of the smaller photo =
`2l+2w`

`=2(5)+2(4)`

`=18` inches

Perimeter of larger photo =
`2l+2w`

`=2(10)+2(8)`

`=36` inches

Ratio:

Perimeter of larger photo : perimeter of smaller photo =
`36:18`

`=2:1`

Area

Area of smaller photo =
`lw`

`=5*4`

`=20` inches²

Area of larger photo =
`lw`

`= 10*8`

`=80` inches ²

Ratio

Area of larger photo : area of smaller photo =
`80:20`

`=4:1`

∴The ratio of the perimeters = 2:1, and the ratio of the areas = 4:1

Hope this helps :)