Triangle A has sides of lengths 51 , 45 , and 33 . 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?

Apr 4, 2018

color(brown)("Case - 1 : " 7, 9.55, 10.82
color(blue)("Case - 2 : " 7, 5.13, 7.93
color(crimson)("Case - 3 : " 7, 4.53, 6.18

Explanation:

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

$\text{Case - 1 : side 7 of " Delta " B corresponds to side 33 of " Delta } A$

$\frac{7}{33} = \frac{b}{45} = \frac{c}{51} , \therefore b = \frac{45 \cdot 7}{33} = 9.55 , c = \frac{51 \cdot 7}{33} = 10.82$

$\text{Case - 2 : side 7 of " Delta " B corresponds to side 45 of " Delta } A$

$\frac{7}{45} = \frac{b}{33} = \frac{c}{51} , \therefore b = \frac{7 \cdot 33}{45} = 5.13 , c = \frac{7 \cdot 51}{45} = 7.93$

$\text{Case - 3 : side 7 of " Delta " B corresponds to side 51 of " Delta } A$

$\frac{7}{51} = \frac{b}{33} = \frac{c}{45} , \therefore b = \frac{7 \cdot 33}{51} = 4.53 , c = \frac{7 \cdot 45}{51} = 6.18$