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.
2a/h -b2=b1

a/2h-b2=b1

2a-b2/h=b1

2a/b1+b2=h

a/2(b1 +b2)=h

Answer 1

Answer:

The equivalent expressions are:

$b1=\frac{2a}{h}-b2$

$h=\frac{2a}{b1+b2}$

Step-by-step explanation:

Given equation for finding area of a trapezoid:

$a=\frac{1}{2}(b1+b2)h$

where $a$ represents area, $h$ represents height and $b1\ and\ b2$ represents the base lengths of the trapezoid.

Evaluating $h$ by rearranging the equation to find an equivalent equation.

Multiplying both sides by 2.

$2\times a=2\times\frac{1}{2}(b1+b2)h$

$2a=(b1+b2)h$

Dividing both sides by $b1+b2$

$\frac{2a}{b1+b2}=\frac{(b1+b2)h}{b1+b2}$

$\frac{2a}{b1+b2}=h$

$\therefore h=\frac{2a}{b1+b2}$

Evaluating $b1$ by rearranging the equation to find an equivalent equation.

Multiplying both sides by 2.

$2\times a=2\times\frac{1}{2}(b1+b2)h$

$2a=(b1+b2)h$

Dividing both sides by $h$

$\frac{2a}{h}=\frac{(b1+b2)h}{h}$

$\frac{2a}{h}=b1+b2$

Subtracting both sides by $b2$

$\frac{2a}{h}-b2=b1+b2-b2$

$\frac{2a}{h}-b2=b1$

$\therefore b1=\frac{2a}{h}-b2$

Answer 2

Answer:

A and D

Step-by-step explanation:

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