Triangle A has sides of lengths #5, 4 #, and #6 #. Triangle B is similar to triangle A and has a side of length #2 #. What are the possible lengths of the other two sides of triangle B?

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Answer 1 · 2018-04-04T03:45:12

#color(green)("Case - 1 : side 2 of " Delta " B corresponds to side 4 of " Delta " A " color(green)(2, 2.5, 3#

#color(blue)("Case - 2 : side 2 of " Delta " B corresponds to side 5 of " Delta " A " 2, 1.6, 2.4#

#color(brown)("Case - 3 : side 2 of " Delta " B corresponds to side 6 of " Delta " A " 2, 1.33, 1.67#

Since triangles A & B are similar, their sides will be in the same proportion.

#"Case - 1 : side 2 of " Delta " B corresponds to side 4 of " Delta " A#

#2 / 4 = b / 5 = c / 6, :. b = (5 8 2) / 4 = 2.5, c = (6 * 2) / 4 = 3#

#"Case - 2 : side 2 of " Delta " B corresponds to side 5 of " Delta " A#

#2 / 5 = b / 4 = c / 6, :. b = 1.6, c = 2.4#

#"Case - 3 : side 2 of " Delta " B corresponds to side 6 of " Delta " A#

#2 / 6 = b / 4 = c / 5, :. b = 1.33, c = 1.67#