Question

Albert's rectangular garden is 6ft by 3ft. He wants to lengthen both dimensions by the same number of feet so that the new area will be 40 square feet. What will be the new dimensions?

Answer 1

8 and 5

Explanation:

Let the number of feet added = x

(x + 6) ( x + 3) = 40 Remove the brackets

x^2 + 6x + 3x + 18 = 40 Combine like terms on the left

x^2 + 9x + 18 = 40 Subtract 18 from both sides

-18 -18

x^2 + 9x = 22 Subtract 22 from both sides

x^2 + 9x - 22 = 0

This quadratic factors

(x + 11)(x - 2)

x + 11 = 0

x = - 11 which makes not sense.

x - 2 = 0

x = 2

The answer is x = 2

Check

6+2 = 8

3+2 = 5

8 * 5 = 4- just as it should.