Question

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

Answer 1

The new dimensions are 5 m by 12 m.

Explanation:

The new dimensions are 3+x m and 10+x m where x is the amount of increase. We have the following system:

A = 3 * 10 = 30 where A is the original area.

2A = (3 + x)(10+x) ( because A was doubled).

Substituting for A = 30 in the second equation:

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

30 + 13x + x^2 = 60

x^2 + 13x - 30 = 0

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

x = -15, 2, x must be positive so we ignore -15.

x = 2 = the increase in the dimensions.

The new dimensions are 3+2 and 10 + 2

= 5 and 12.