Question

if $\triangle xyz \sim \triangle ayb$, and $yz = 100$ cm, $ya = 12$ cm, and $yb = 16$ cm, then what is the length of $yx$? (1 point) \bigcirc 32 cm \bigcirc 117 cm \bigcirc 53 cm \bigcirc 75 cm

Explanation:

Step1: Recall Similar Triangles Property

For similar triangles \( \triangle XYZ \sim \triangle AYB \), the corresponding sides are proportional. So, \( \frac{YX}{YA}=\frac{YZ}{YB} \).

Step2: Substitute Known Values

We know \( YZ = 100 \, \text{cm} \), \( YA = 12 \, \text{cm} \), \( YB = 16 \, \text{cm} \). Substitute into the proportion: \( \frac{YX}{12}=\frac{100}{16} \).

Step3: Solve for \( YX \)

Cross - multiply: \( YX\times16 = 12\times100 \). Then \( YX=\frac{12\times100}{16} \). Simplify \( \frac{1200}{16}=75 \, \text{cm} \).

Answer:

75 cm