Triangle A has sides of lengths #28 #, #32 #, and #24 #. Triangle B is similar to triangle A and has a side of length #4 #. What are the possible lengths of the other two sides of triangle B?

1 Answer
Mar 3, 2018

Case 1 : sides of Triangle B #4, 4.57, 3.43#

Case 2 : sides of Triangle B #3.5, 4, 3#

Case 3 : sides of Triangle B #4.67, 5.33, 4#

Explanation:

Triangle A with sides #p = 28, q = 32, r = 24#

Triangle B with sides #x, y, z#

http://www.algebraden.com/three-sided-polygon-triangle.htm

http://www.ontrack-media.net/geometry/Geometry%20Tests/gm4l15atest.html

Given both the sides are similar.

Case 1. Side x = 4 of triangle B proportional to p of triangle A.

# 4 / 28 = y / 32 = z / 24#

#y = (4 * 32) / 28 = 4.57#

#z = (4 * 24) / 28 = 3.43#

Case 2 : Side y = 4 of triangle B proportional to q of triangle A.

# x / 28 = 4 / 32 = z / 24#

#x = (4 * 28) / 32 = 3.5#

#z = (4 * 24) / 32 = 3#

Case 3 : Side z = 4 of triangle B proportional to r of triangle A.

# x / 28 = y / 32 = 4 / 24#

#x = (4 * 28) / 24 = 4.67#

#y = (4 * 32) / 24 = 5.33#