# Triangle A has sides of lengths 2 ,3 , and 4 . Triangle B is similar to triangle A and has a side of length 5 . What are the possible lengths of the other two sides of triangle B?

Triangle $1 : \text{ } 5 , \frac{15}{2} , 10$
Triangle $2 : \text{ } \frac{10}{3} , 5 , \frac{20}{3}$
Triangle $3 : \text{ } \frac{5}{2} , \frac{15}{4} , 5$

#### Explanation:

Given : triangle A: sides 2, 3, 4, use ratio and proportion to solve for the possibles sides

For example: Let the other sides of triangle B represented by x, y,z
If $x = 5$ find y

$\frac{y}{3} = \frac{x}{2}$

$\frac{y}{3} = \frac{5}{2}$

$y = \frac{15}{2}$

solve for z:

$\frac{z}{4} = \frac{x}{2}$
$\frac{z}{4} = \frac{5}{2}$
$z = \frac{20}{2} = 10$

that completes triangle 1:

For triangle $1 : \text{ } 5 , \frac{15}{2} , 10$

use scale factor $= \frac{5}{2}$ to obtain the sides $5 , \frac{15}{2} , 10$

Triangle $2 : \text{ } \frac{10}{3} , 5 , \frac{20}{3}$

use scale factor $= \frac{5}{3}$ to obtain the sides $\frac{10}{3} , 5 , \frac{20}{3}$

Triangle $3 : \text{ } \frac{5}{2} , \frac{15}{4} , 5$
use scale factor $= \frac{5}{4}$ to obtain the sides $\frac{5}{2} , \frac{15}{4} , 5$

God bless...I hope the explanation is useful.