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?

Apr 4, 2018

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

Explanation:

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

$\text{Case - 1 : side 2 of " Delta " B corresponds to side 4 of " Delta } A$

$\frac{2}{4} = \frac{b}{5} = \frac{c}{6} , \therefore b = \frac{5 8 2}{4} = 2.5 , c = \frac{6 \cdot 2}{4} = 3$

$\text{Case - 2 : side 2 of " Delta " B corresponds to side 5 of " Delta } A$

$\frac{2}{5} = \frac{b}{4} = \frac{c}{6} , \therefore b = 1.6 , c = 2.4$

$\text{Case - 3 : side 2 of " Delta " B corresponds to side 6 of " Delta } A$

$\frac{2}{6} = \frac{b}{4} = \frac{c}{5} , \therefore b = 1.33 , c = 1.67$