Question

The ratio of the width to the length of a rectangle is 2:3, respectively. Answer each of the following. a By what percent would the area of the rectangle change if the width of the rectangle is increased by 50% and the length is increased by the same number of units?

Answer 1

Answer: 125%

Step-by-step explanation:

The ratio of the width to the length of a rectangle is 2:3, respectively , this means that :

W = $\frac{2}{3}$L

Area of a rectangle = Length X Width , this means that

A = L X $\frac{2}{3}$L

A = $\frac{2}{3}$$L^{2}$

The Length and the Width increased by 50% , this means that :

New Length = 1.5L

New Width = 1.5W

New area = 1.5L x 1.5 W

New area = 2.25WL

But W = $\frac{2}{3}$L , therefore :

New Area = 2.25L( $\frac{2}{3}$L )

New Area = 1.5$L^{2}$

Therefore , % change in area = change in area / original area x 100

Change in area = 1.5$L^{2}$ - $\frac{2}{3}$$L^{2}$

% change in area = 0.833/0.677 x 100

% change in area = 125%