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Area
=
qquad
3 Find the missing parallel side of the trapezoid with an area of
200in^(2)
qquad
X=
qquad

9ft
X

Area $=$ $\qquad$ $\newline$ $3$ Find the missing parallel side of the trapezoid with an area of $200 \mathrm{in}^{2}$ $\qquad$ $\mathrm{X}=$ $\qquad$ $\newline$ $9 \mathrm{ft}$ $\newline$ X

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Find derivatives using the quotient rule II

Full solution

Q. Area

=

\qquad

\newline

3

Find the missing parallel side of the trapezoid with an area of

200 \mathrm{in}^{2}

\qquad

\mathrm{X}=

\qquad

\newline

9 \mathrm{ft}

\newline

X

Convert to inches: To find the missing parallel side of the trapezoid, we need to use the area formula for a trapezoid, which is $A = \frac{1}{2}(b_1 + b_2)h$ , where $A$ is the area, $b_1$ and $b_2$ are the lengths of the two parallel sides, and $h$ is the height. We know the area ( $200 \text{ in}^2$ ), one parallel side ( $9 \text{ ft}$ ), and the height ( $3 \text{ ft}$ ). First, we need to convert all measurements to the same unit. Let's convert $9 \text{ ft}$ to inches because the area is given in square inches. There are $12$ inches in a foot, so $9 \text{ ft}$ is $A$ $1$ inches.
Calculate $b_1$ : Now, we calculate $9$ ft in inches: $9 \times 12 = 108$ inches. So, $b_1 = 108$ inches. We can now plug the values into the area formula and solve for $b_2$ .
Plug values and solve: Plugging the values into the area formula: $200 = \left(\frac{1}{2}\right)(108 + b_2) \times 3$ . Now, we need to solve for $b_2$ .
Multiply by $2$ : First, multiply both sides by $2$ to get rid of the fraction: $400 = (108 + b_2) \times 3$ .
Divide by $3$ : Next, divide both sides by $3$ to isolate the term with $b^2$ : $\frac{400}{3} = 108 + b^2$ .
Calculate result: Now, we calculate $400 / 3$ : $400 / 3 = 133.33$ . So, $133.33 = 108 + b_2$ .
Subtract $108$ : Subtract $108$ from both sides to find $b_2$ : $133.33 - 108 = b_2$ .
Calculate $b_2$ : Finally, we calculate $b_2$ : $133.33 - 108 = 25.33$ inches. So, the missing parallel side $b_2$ is $25.33$ inches.

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