Question

the area of a parallelogram is 96 cm². the height of the parallelogram is 4 cm less than the length of the base. what is the length of the base? a 5 cm b 8 cm c 12 cm d 14 cm

Explanation:

Step1: Set up the base - height relationship

Let the length of the base be $x$ cm. Then the height is $(x - 4)$ cm.

Step2: Use the area formula of a parallelogram

The area formula of a parallelogram is $A=bh$, where $A$ is the area, $b$ is the base, and $h$ is the height. Given $A = 96$ cm², we have the equation $x(x - 4)=96$.

Step3: Expand the equation

Expand $x(x - 4)$ to get $x^{2}-4x=96$, then rewrite it as a quadratic equation $x^{2}-4x - 96=0$.

Step4: Factor the quadratic equation

Factor $x^{2}-4x - 96$ as $(x - 12)(x + 8)=0$.

Step5: Solve for $x$

Set each factor equal to zero: $x-12 = 0$ gives $x = 12$, and $x + 8=0$ gives $x=-8$. Since the length cannot be negative, we discard $x=-8$.

Answer:

C. 12 cm