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 = $\frac{1}{2}(b_1 + b_2 )h$ 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) $\frac{2a}{h} - b_2 = b_1$

(b) $\frac{a}{2h} - b_2 = b_1$

(c) $\frac{2a - b_2}{h}$ = $b_1$

(d) $\frac{2a}{b_1 + b_2} = h$

(e) $\frac{a}{2(b_1 + b_2)}$ = h

Answer: (a) $\frac{2a}{h} - b_2 = b_1$; (d) $\frac{2a}{b_1 + b_2} = h$;

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

a = $\frac{1}{2}(b_1 + b_2 )h$

2a = ($b_1 + b_2$)h

$\frac{2a}{h} = b_1 + b_2$

$\frac{2a}{h} - b_2 = b_1$

To determine h:

a = $\frac{1}{2}(b_1 + b_2 )h$

2a = $(b_1 + b_2)h$

$\frac{2a}{(b_1 + b_2)}$ = h

To determine $b_2$

a = $\frac{1}{2}(b_1 + b_2 )h$

2a = $(b_1 + b_2)h$

$\frac{2a}{h} = (b_1 + b_2)$

$\frac{2a}{h} - b_1 = b_2$

Checking the alternatives, you have that $\frac{2a}{h} - b_2 = b_1$ and $\frac{2a}{(b_1 + b_2)}$ = h, so alternatives A and D are correct.