Question

The area of the trapezoid is $\left(\frac{3}{4}x-\frac{1}{4}\right)$ square centimeters. Write two different pairs of expressions that represent the possible base lengths (in centimeters). Justify your answers.

Answer 1

Hint: Area of the trapezoid =$height\times \frac{sumofparallellenghts}{2}$

Step 1: As we know

Area of the trapezoid =$height\times \frac{sumofparallellenghts}{2}$

Given area of trapezoid =

$$\begin{gathered} \left(\frac{3}{4}x-\frac{1}{4}\right) \\ =\left(\frac{3}{2}\times \frac{1}{2}x-\frac{1}{2}\times \frac{1}{2}\right)\left\{Factorize\right\} \\ =\left(\frac{3x-1}{2}\right)\frac{1}{2}\{Distributiveproperty\} \end{gathered}$$

By comparing we get height is $\frac{1}{2}$

and base length is $\left(\frac{3x-1}{2}\right)$

Final Answer: Base lenght is $\left(\frac{3x-1}{2}\right)$