Triangle A has sides of lengths #48 ,24 #, and #27 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #48     ,24   #, and #27   #. Triangle B is similar to triangle A and has a side of length #5   #. What are the possible lengths of the other two sides of triangle B?

Claire Akin · Accepted Answer

Possible lengths of the triangle B are
Case (1) : 5, 5.625, 10

Case (2) : 5, 4.44, 8.89

Are (3) : 5, 2.5, 2.8125

Triangles A & B are similar. Case (1) #:.5/24=b/27=c/48# #b=(5*27)/24= 5.625# #c=(5*48)/24= 10# Possible lengths of other two sides of triangle B are #5, 5.625, 10# Case (2) #:.5/27=b/27=c/48# #b=(5*24)/27=4.44# #c=(5*48)/27=8.89# Possible lengths of other two sides of triangle B are #5, 4.44, 8.89# Case (3) #:.5/48=b/24=c/27# #b=(5*24)/48=2.5# #c=(5*27)/48=2.8125# Possible lengths of other two sides of triangle B are #5, 2.5, 2.8125#

Violet Aldrich · Answer

undefined To find the possible lengths of the other two sides of Triangle B, which is similar to Triangle A:

1. Determine the scale factor between the corresponding sides of Triangle A and Triangle B. Scale factor = Length of corresponding side in Triangle B / Length of corresponding side in Triangle A.
2. Use the scale factor to find the lengths of the other two sides of Triangle B.

Given:
Length of the side in Triangle B = 5

Scale factor = 5 / 48 ≈ 0.1042 (Using the length of the shortest sides of both triangles)

Possible lengths of the other two sides of Triangle B:
Side 1: 24 * 0.1042 ≈ 2.5008
Side 2: 27 * 0.1042 ≈ 2.8124