Question

The equation a=1/2(b^1+b^2)h can be determined the area, a, of a trapezoid with height, h, and base lengths, b^1 and b^2 Which are equivalent equations?

Answer 1

The complete question is as follows.

The equation a =
`(1)/(2)(b_1 + b_2 )h` can be used to determine the area , a, of a trapezoid with height , h, and base lengths,
`b_1` and
`b_2`. Which are equivalent equations?

(a)
`(2a)/(h) - b_2 = b_1`

(b)
`(a)/(2h) - b_2 = b_1`

(c)
`(2a - b_2)/(h)` =
`b_1`

(d)
`(2a)/(b_1 + b_2) = h`

(e)
`(a)/(2(b_1 + b_2))` = h

Answer: (a)
`(2a)/(h) - b_2 = b_1`; (d)
`(2a)/(b_1 + b_2) = h`;

Step-by-step explanation: To determine
`b_1`:

a =
`(1)/(2)(b_1 + b_2 )h`

2a = (
`b_1 + b_2`)h

`(2a)/(h) = b_1 + b_2`

`(2a)/(h) - b_2 = b_1`

To determine h:

a =
`(1)/(2)(b_1 + b_2 )h`

2a =
`(b_1 + b_2)h`

`(2a)/((b_1 + b_2))` = h

To determine
`b_2`

a =
`(1)/(2)(b_1 + b_2 )h`

2a =
`(b_1 + b_2)h`

`(2a)/(h) = (b_1 + b_2)`

`(2a)/(h) - b_1 = b_2`

Checking the alternatives, you have that
`(2a)/(h) - b_2 = b_1` and
`(2a)/((b_1 + b_2))` = h, so alternatives A and D are correct.