a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x+5) x=104 represents the situation, where x represents the width of the rectangle. (x+5) x=104 x2+5x-104=0. Determine the solutions of the equation. What solution makes sense for the situation?

x=8

Step-by-step explanation:

Area of a rectangle=length*width

Area=104

Width=x

Length=5+x

104=x * (5+x)

104=5x+x^2

104-5x-x^2=0

x^2+5x-104=0

Can also be written as

-x^2-5x+104=0

Solve the quadratic equation using formula

-x2-5x+104=0

using the Quadratic Formula where

a = - 1, b = - 5, and c = 104

x=-b±√b2-4ac/2a

x = - (-5) ±√ (-5) 2-4 (-1) (104) / 2 (-1)

x=5±√25 - (-416) / -2

x=5±√441/-2

The discriminant b^2-4ac>0

so, there are two real roots.

Simplify the Radical:

x=5±21/-2

x=-26/2 or 16/2

x=-13 or 8

The value of x can't be negative

So, x=8 is the answer