Triangle A has sides of lengths #60 #, #42 #, and #60 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?

1 Answer
Jun 10, 2016

#10 and 4.9#

Explanation:

#color(white)(WWWW)color (black)Delta B"color(white)(WWWWWWWWWWWWWW)color (black)Delta A#
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Let two triangles #A and B# be similar. #DeltaA# is #OPQ# and has sides #60,42 and 60#. Since two sides are equal to each other it is an isosceles triangle.
and #DeltaB# is #LMN# has one side#=7#.
By properties of Similar Triangles

  1. Corresponding angles are equal and
  2. Corresponding sides are all in the same proportion.

It follows that #DeltaB# must also be an isosceles triangle.

There are two possibilities
(a) Base of #DeltaB# is #=7#.
From proportionality
#"Base"_A/"Base"_B="Leg"_A/"Leg"_B# .....(1)
Inserting given values
#42/7=60/"Leg"_B#
#=>"Leg"_B=60xx7/42#
#=>"Leg"_B=10#

(b) Leg of #DeltaB# is #=7#.
From equation (1)
#42/"Base"_B=60/7#
#"Base"_B=42xx7/60#
#"Base"_B=4.9#