Question

The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lengths of the bases of the trapezoid? The area of the triangle is 65 cm squared

Answer 1

`b_1 \approx 7.2`

`b_2 \approx 14.4`

Explanation:

Given

`Area = 65cm^2` --- Area of the triangle

`b_2 = 2b_1` --- the bases of the trapezoid

The missing parameters is:

`h=6 cm` --- Trapezoid height

Required

Determine b1 and b2

Since the areas of the trapezoid and the triangle are the same, then:

`Area = (1)/(2)(b_1 + b_2) *h`

So, we have:

`65 = (1)/(2)(b_1 +b_2) * 6`

Substitute
`b_2 = 2b_1`

`65 = (1)/(2)(b_1 +2b_1) * 6`

`65 = (1)/(2)(3b_1) * 6`

`65 = 3b_1 * 3`

`65 = 9b_1`

Solve for
`b_1`

`b_1 = (65)/(9)`

`b_1 \approx 7.2`

Substitute
`b_1 \approx 7.2` in
`b_2 = 2b_1`

`b_2 \approx 2 * 7.2`

`b_2 \approx 14.4`