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

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

Step-by-step 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