Answer:
one base is 9 inches and other is 15 inches.
Step-by-step explanation:
Given : The height of a trapezoid is 8 inches and its area is 96 in one base of the trapezoid is 6 inches longer than the other base.
We have to find the lengths of the bases.
We know area of trapezoid \(=\frac{1}{2} \times \text{Sum of parallel sides} \times \text{height}\)
Given : area of trapezoid = 96 inches²,
Height is 8 inches
and one base of the trapezoid is 6 inches longer than the other base.
Let one base be x , then other will be 6 + x
Substitute in formula, we have,
\(96=\frac{1}{2}\times {(x+6+x)} \times 8\)
Solving we get,
\(96=\frac{1}{2}\times {(2x+6)} \times 8\)
⇒ 96 = (2x+ 6) × 4
Divide both side by 4, we have
⇒ 24 = (2x+6)
Subtract 6 both side, we have
⇒ 18 = 2x
Solve for x, we have,
⇒ x = 9
Thus, one base is 9 inches and other is 15 inches.
