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

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.