Question

The dimensions of a rectangular garden were 3m by 10m. When both dimensions were increased by equal amounts, the area of the garden doubled. Find the dimensions of the new garden

Answer 1

The answer to your question is: New dimensions = 5 and 12

Explanation:

Process

1.- Find the area of the first triangle

A = 3 x 10

A = 30 m²

2.- Consider that the length of the sides of the rectangle increase by "x".

base = 3 + x

height = 10 + x

3.- Calculate the value of "x"

New area = 2(30) = 60 m²

60 = (x + 3) (x + 10)

60 = x² + 13x + 30

0 = x² + 13x + 30 - 60

0 = x² + 13x - 30

Factor

0 = (x + 15)(x - 2)

x₁ = -15 x₂ = 2

4.- Find the new dimensions

New base = 10 + 2 = 12 m

New height = 3 + 2 = 5 m