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

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

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,

Solving we get,

⇒ 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.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2