Algebra 1 question please help

Question

Write an expression that describes the area of the rectangle if the length is 2x+3 and the width x+5

A. (2x+3)(x+5)

B. 2(2x+3)(x+5)

C. 2(2x+3) + 2(x+5)

D. 2(2x+3) + (x + 5)

If the area of the rectangle is 72 squared inches determine the value of x.

Answer 1

To find the area of a rectangle, just multiply the length and the width.

If the area is 72, then you multiply the length and the width and set it equal to 72:

(2x + 3)(x + 5) = 72 [now multiply out the left side of the equation

2x² + 10x + 3x + 15 = 72 [To solve a quadratic, set it equal to zero. To do so, subtract 72 from both sides:

2x² + 10x + 3x + 15 - 72 = 0 [combine like terms:

2x² + 13x - 57 [Factor the quadratic:

(x - 3)(2x + 19) = 0 [Set each piece equal to zero:

x - 3 = 0 (x = 3) or 2x + 19 = 0 (x = -19/2)

Plugging in these values of "x" into "2x + 3" and "x + 5", we see that x = -19/2 gives us a negative length. Since that is not possible for a rectangle, we can throw that answer out in this case. So x = 3