Triangle A has sides of lengths #24 #, #15 #, and #21 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?

1 Answer
Feb 1, 2018

Case 1 : #color(green)(24, 15,21# Both are identical triangles

Case 2 : #color(blue)(24, 38.4, 33.6#

Case 3 : #color(red)(24, 27.4286, 17.1429#

Explanation:

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Given :Triangle A (#DeltaPQR#) similar to Triangle B #(DeltaXYZ)#

#PQ = r = 24, QR = p = 15, RP = q = 21#

Case 1 : #XY = z = 24#

Then using similar triangles property,

#r / z = p / x = q / y#

#24 / 24 = 15 / x = 21 / y#

#:. x = 15, y = 21#

Case 2 : #YZ = x = 24#

#24 / z = 15 / 24 = 21 / y#

#z = (24 * 24) / 15 = 38.4#

#y = (21 * 24) / 15 = 33.6#

Case 2 : #ZX = y = 24#

#24 / z = 15 / x = 21 / 24#

#z = (24 * 24) / 21 = 27.4286#

#y = (15 * 24) / 21 = 17.1429#