Question

triangle pqr is dilated to produce similar △jkl. write a proportion you can use to determine the value of x. select all that apply.
8 cm 10 cm 4 cm 5 cm
15 cm
□ $\frac{15}{x}=\frac{5}{10}$
□ $\frac{x}{15}=\frac{5}{10}$
□ $\frac{x}{15}=\frac{8}{4}$
□ $\frac{4}{8}=\frac{x}{15}$

Explanation:

Step1: Recall similarity - side - ratio property

For similar triangles, the ratios of corresponding sides are equal.

Step2: Identify corresponding sides

In similar triangles $\triangle PQR$ and $\triangle JKL$, side $PR = 15$ cm corresponds to side $JL=x$ cm, side $QR = 10$ cm corresponds to side $KL = 5$ cm, and side $PQ=8$ cm corresponds to side $JK = 4$ cm.
The ratio of corresponding sides gives the following proportions:

• $\frac{PR}{JL}=\frac{QR}{KL}$, so $\frac{15}{x}=\frac{10}{5}$ which can be rewritten as $\frac{x}{15}=\frac{5}{10}$.
• Also, $\frac{PQ}{JK}=\frac{PR}{JL}$, so $\frac{8}{4}=\frac{15}{x}$ which can be rewritten as $\frac{4}{8}=\frac{x}{15}$.

Answer:

$\frac{x}{15}=\frac{5}{10}$, $\frac{4}{8}=\frac{x}{15}$