In similar triangles JKL and WXY, the ratio of the length of side JK to the length of its … — SAT

In similar triangles $JKL$ and $WXY$ , the ratio of the length of side $JK$ to the length of its corresponding side $WX$ is $1$ to $4$ . If the length of side $WX$ is $x + 9$ and the length of side $JK$ is $x$ , what is the value of $x$ ?

Answer: 3

Answer

The correct answer is 3.

Because triangles

JKL

and

WXY

are similar, the ratio of corresponding side lengths is constant. Since the ratio of

JK

WX

1

4

, the relationship can be written as

\frac{x}{x + 9} = \frac{1}{4}

. Cross-multiplying yields

4x = x + 9

. Subtracting

x

from both sides gives

3x = 9

, and dividing by

3

gives the final answer

x = 3

Step-by-Step Solution

Set up a proportion using the ratio of corresponding side lengths.

\frac{x}{x + 9} = \frac{1}{4}

The ratio of corresponding side lengths in similar triangles is constant.

Cross-multiply to eliminate fractions.

4x = x + 9

Multiplying both sides by both denominators simplifies the equation.

Solve for the variable

x

x = 3

Subtracting

x

from both sides gives

3x = 9

, and dividing by

3

gives

x = 3

Key Concept

The corresponding side lengths of similar triangles are proportional.

Question

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Step-by-Step Solution

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