Math / Geometry

Question $\text{Find the value of } X \text{ in each pair of similar figures.}$ $\text{Given:}$ $S = 15 \text{ in, } R = 20, \text{ and } T = X$ $N = L = 20 \text{ in, } M = 12 \text{ in}$ $\text{Assume the figures are similar and use the proportions to solve for } X.$

Studdy Solution

STEP 1

1. The figures are similar, meaning corresponding sides are proportional.
2. The side $QR$ in parallelogram $SQRT$ corresponds to side $LM$ in parallelogram $LMNO$ .
3. The side $RT$ in parallelogram $SQRT$ corresponds to side $MO$ in parallelogram $LMNO$ .
4. We need to find the value of $X$ which is the length of side $RT$ .

STEP 2

1. Set up the proportion based on the similarity of the figures.
2. Solve the proportion for $X$ .

STEP 3

Set up the proportion using the corresponding sides of the similar figures:
$\frac{QR}{LM} = \frac{RT}{MO}$
Substitute the given values:
$\frac{15}{20} = \frac{X}{12}$

STEP 4

Solve the proportion for $X$ :
First, cross-multiply to solve for $X$ :
$15 \times 12 = 20 \times X$
Simplify the equation:
$180 = 20X$
Divide both sides by 20 to solve for $X$ :
$X = \frac{180}{20}$
Calculate the value:
$X = 9$
The value of $X$ is:
$\boxed{9}$

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