Question

The equation a = StartFraction one-half EndFraction left-parenthesis b 1 plus b 1 right-parenthesis.(b1 + b2)h can be used to determine the area, a, of a trapezoid with height, h, and base lengths, b1 and b2. Which are equivalent equations? Check all that apply.

StartFraction 2 a Over h EndFraction minus b 2 equals b 1.– b2 = b1
StartFraction a Over 2 h EndFraction minus b 2 equals b 1. – b2 = b1
StartFraction 2 a minus b 2 Over h EndFraction equals b. = b1
StartFraction 2 a Over b 1 plus b 2 EndFraction equals h. = h
StartFraction a Over 2 left-parenthesis b 1 plus b 1 right-parenthesis EndFraction equals h.= h

Answer 1

Start with a = (1/2)(b1 + b2)h.
Multiply both sides by 2: 2a = (b1 + b2)h.

Solve for b1:
2a/h = b1 + b2 => b1 = 2a/h − b2.

Solve for h:
h = 2a/(b1 + b2).

Now check the choices:
- (2a/h) − b2 = b1 — equivalent (correct).
- a/(2h) − b2 = b1 — not equivalent (wrong factor).
- (2a − b2)/h = b1 — not equivalent (algebraically wrong).
- 2a/(b1 + b2) = h — equivalent (correct).
- a/[2(b1 + b2)] = h (or a/[2(b1 + b1)] as printed) — not equivalent.

So the equivalent equations are the first and the fourth.