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

Answer:

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

Step-by-step 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:

$\frac{A_{re}}{A_{sq}} = \frac{(1.5\cdot l)\cdot (0.5\cdot l)}{l^{2}}$

$\frac{A_{re}}{A_{sq}} = 0.75$

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