Question

The length of each side of square A is increased by 100 percent to make square B. Then each side of square is increased by 50 percent to make square C. By what percent is the area of square C greater than the sum of the areas of square A and B?

Answer 1

Area of C is `80%` greater than area of A `+` area of B

Explanation:

Define as a unit of measurement the length of one side of A.

Area of A `= 1^2 = 1` sq.unit

Length of sides of B is `100%` more than length of sides of A
`rarr` Length of sides of B `=2` units
Area of B `=2^2 = 4` sq.units.

Length of sides of C is `50%` more than the length of sides of B
`rarr` Length of sides of C `=3` units
Area of C `=3^2 = 9` sq.units

Area of C is `9-(1+4) = 4` sq.units greater than the combined areas of A and B.

`4` sq.units represents `4/(1+4)=4/5` of the combined area of A and B.

`4/5 = 80%`