Question

Suppose the area of a Little Italy gallery is 588 square meters and has a rectangular shape. If one side of the gallery measures 2x + 4 and another side measures 8x + 2, what is the value of x?

Answer 1

2x + 4 + 8x + 2 + x = 0

11x + 6 = 0

11x = -6

x = -6 /11

Answer 2

Answer:

x = 5

Step-by-step explanation:

A = l*b

Therefore, 588 = (2x+4)(8x+2)

                  588 = 2(x + 2)*2(4x+1)

                  $\frac{588}{4}$   = (x+2)(4x+1)

                  147  = 4$x^2$ + 9x + 2

                  4$x^2$ + 9x - 145 = 0

                  4$x^2$ -20x + 29x -145 = 0

                  4x(x -5) + 29(x - 5) = 0

                  (4x + 29)(x - 5) = 0

Therefore,  either 4x + 29 = 0 or (x - 5) = 0

Therefore, x = $\frac{-29}{4}$ or x = 5

But, x denotes length, which can never be negative

Therefore, x = 5