# Triangle A has sides of lengths 24 , 15 , and 21 . Triangle B is similar to triangle A and has a side of length 24 . What are the possible lengths of the other two sides of triangle B?

Feb 1, 2018

Case 1 : color(green)(24, 15,21 Both are identical triangles

Case 2 : color(blue)(24, 38.4, 33.6

Case 3 : color(red)(24, 27.4286, 17.1429

#### Explanation:

Given :Triangle A ($\Delta P Q R$) similar to Triangle B $\left(\Delta X Y Z\right)$

$P Q = r = 24 , Q R = p = 15 , R P = q = 21$

Case 1 : $X Y = z = 24$

Then using similar triangles property,

$\frac{r}{z} = \frac{p}{x} = \frac{q}{y}$

$\frac{24}{24} = \frac{15}{x} = \frac{21}{y}$

$\therefore x = 15 , y = 21$

Case 2 : $Y Z = x = 24$

$\frac{24}{z} = \frac{15}{24} = \frac{21}{y}$

$z = \frac{24 \cdot 24}{15} = 38.4$

$y = \frac{21 \cdot 24}{15} = 33.6$

Case 2 : $Z X = y = 24$

$\frac{24}{z} = \frac{15}{x} = \frac{21}{24}$

$z = \frac{24 \cdot 24}{21} = 27.4286$

$y = \frac{15 \cdot 24}{21} = 17.1429$