Question

triangle fgh is similar to triangle klm. some of the side lengths of the two triangles are shown.

• fg = 18 centimeters
• kl = 12 centimeters
• hf = 21 centimeters

what is mk, in centimeters?

Explanation:

Step1: Recall Similar Triangles Property

For similar triangles \( \triangle FGH \) and \( \triangle KLM \), corresponding sides are proportional. So, \( \frac{FG}{KL}=\frac{HF}{MK} \).

Step2: Substitute Known Values

We know \( FG = 18 \), \( KL = 12 \), \( HF = 21 \). Substitute into the proportion: \( \frac{18}{12}=\frac{21}{MK} \).

Step3: Solve for \( MK \)

Cross - multiply: \( 18\times MK=12\times21 \). Calculate \( 12\times21 = 252 \). Then \( MK=\frac{12\times21}{18} \). Simplify \( \frac{252}{18}=14 \).

Answer:

14