Question

A rectangle is formed from a square by increasing the latter's length by 50% while reducing its width by 50%. The ratio of the area of the rectangle to that of the square is ?

Answer 1

The ratio of the area of the rectangle to the area of the square is 0.75.

Explanation:

The areas of the square and the rectangle are represented by following formulas:

`A_(sq) = l^(2)` (1)

`A_(re) = (1.5\cdot l)\cdot (0.5\cdot l)` (2)

Where
`l` is the side length of the square.

The ratio of the area of the rectangle to the area of the square is:

`(A_(re))/(A_(sq)) = ((1.5\cdot l)\cdot (0.5\cdot l))/(l^(2))`

`(A_(re))/(A_(sq)) = 0.75`

The ratio of the area of the rectangle to the area of the square is 0.75.