Question

The area of the trapezoid is {(3/4)x-(1/4)x} square centimeters. Write two different pairs of expressions that represent the possible base lengths (in centimeters).

Answer 1

The possible base lengths (in centimeters) of the trapezoid can be represented by two different pairs of expressions: (3/4)x and -(1/4)x, or -(1/4)x and (3/4)x.

Step-by-step explanation:

To find the base lengths of the trapezoid, we need to equate the given expression to the formula for the area of a trapezoid. The formula for the area of a trapezoid is: Area = (1/2) x (base1 + base2) x height. We can set this equal to the given expression and solve for base1 and base2. Taking the given expression {(3/4)x-(1/4)x}, we can write two different pairs of expressions for base1 and base2:

1. base1 = (3/4)x and base2 = -(1/4)x
2. base1 = -(1/4)x and base2 = (3/4)x

These two pairs of expressions represent the possible base lengths (in centimeters) of the trapezoid.