Question

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 what are the lengths of the bases explain how you found your answer

Answer 1

one base is 9 inches and other is 15 inches.

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
`=(1)/(2) * \text{Sum of parallel sides} * \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=(1)/(2)* {(x+6+x)} * 8`

Solving we get,

`96=(1)/(2)* {(2x+6)} * 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.

Answer 2

First is to get the given data that we might be able to use for computation.
H = 8 inches
Area = 96
B1 = B1
B2 = B1+6

Next is to know the area of a trapezoid
Area = H x (B1 + B2)/2
96 = 8 x (B1 + B1 + 6) / 2
96 = 8 x (2B1 + 6) /2
96 = 4 x (2B1 + 6)
14 = 2B1 + 6
2B1 = 8
B1 = 4
B2 = 10