Question

triangle klm is similar to triangle pqr.
image of two triangles: triangle klm with kl = 60 ft, lm = 80 ft; triangle pqr with qr = 40 ft, pr = 60 ft
what is the length of side km?
a. 60 ft
b. 80 ft
c. 100 ft
d. 120 ft

Explanation:

Step1: Find the scale factor

First, identify the corresponding sides. In similar triangles, the ratio of corresponding sides is equal. Let's find the ratio of side \( LM \) (80 ft) to side \( QR \) (40 ft). The scale factor \( k \) is \( \frac{LM}{QR}=\frac{80}{40} = 2 \).

Step2: Calculate \( KM \)

Now, the side \( PR \) in triangle \( PQR \) is 60 ft, and \( KM \) in triangle \( KLM \) corresponds to \( PR \). So we multiply the length of \( PR \) by the scale factor. \( KM=PR\times k = 60\times2 = 120 \) ft.

Answer:

D. 120 ft