# Triangle A has sides of lengths 28 , 32 , and 24 . Triangle B is similar to triangle A and has a side of length 4 . What are the possible lengths of the other two sides of triangle B?

Mar 3, 2018

Case 1 : sides of Triangle B $4 , 4.57 , 3.43$

Case 2 : sides of Triangle B $3.5 , 4 , 3$

Case 3 : sides of Triangle B $4.67 , 5.33 , 4$

#### Explanation:

Triangle A with sides $p = 28 , q = 32 , r = 24$

Triangle B with sides $x , y , z$

Given both the sides are similar.

Case 1. Side x = 4 of triangle B proportional to p of triangle A.

$\frac{4}{28} = \frac{y}{32} = \frac{z}{24}$

$y = \frac{4 \cdot 32}{28} = 4.57$

$z = \frac{4 \cdot 24}{28} = 3.43$

Case 2 : Side y = 4 of triangle B proportional to q of triangle A.

$\frac{x}{28} = \frac{4}{32} = \frac{z}{24}$

$x = \frac{4 \cdot 28}{32} = 3.5$

$z = \frac{4 \cdot 24}{32} = 3$

Case 3 : Side z = 4 of triangle B proportional to r of triangle A.

$\frac{x}{28} = \frac{y}{32} = \frac{4}{24}$

$x = \frac{4 \cdot 28}{24} = 4.67$

$y = \frac{4 \cdot 32}{24} = 5.33$