algebra - graphs

Question

The area of a rectangle is given by A(x)=x^2+5x with x being the height and x+5 being the base. If the area is 14, what is the only viable solution for the height? why are there not 2 solutions

Answer 1

Area = length x width

x²+5x=x(x+5)

Plugging in the area

14=x(x+5)

Distributive property on the right

14=x²+5x

To solve, subtract 14 from each side

0=x²+5x-14

Factor

0=(x+7)(x-2)

Setting both factors equal to zero and solving

x+7=0 and x-2 = 0

x=-7 and x=2 are 2 solutions. However -7 is not a valid height for a rectangle, it must be positive.

The height must be 2