Question

the area of a rectangle is 24 square centimeters. the length (x, in centimeters) of the rectangle is given by the equation x² + 5x = 24. what is the length of the rectangle?
a 3 cm
b 5 cm
c 8 cm
d 12 cm

Explanation:

Step1: Rearrange the equation

We have the quadratic equation $x^{2}+5x = 24$, which can be rewritten as $x^{2}+5x - 24=0$.

Step2: Factor the quadratic equation

The quadratic $x^{2}+5x - 24$ factors to $(x + 8)(x - 3)=0$ since $8\times(- 3)=-24$ and $8+( - 3)=5$.

Step3: Solve for x

Setting each factor equal to zero gives $x+8 = 0$ or $x - 3=0$. So $x=-8$ or $x = 3$. Since length cannot be negative, we take $x = 3$.

Answer:

A. 3 cm