Triangle A has sides of lengths 48 ,36 , and 54 . Triangle B is similar to triangle A and has a side of length 14 . What are the possible lengths of the other two sides of triangle B?

Aug 4, 2018

color(crimson)("Possible lengths of other two sides of triangle b are "

color(indigo)((i) 28/3, 63/4,color(chocolate)((ii) 56/3, 21, color(blue)((iii) 112/9, 28/3

Explanation:

$\text{in " Delta A : a = 48, b = 36, c = 54, " in " Delta B : " one side } = 14$

$\text{When side 14 of triangle B corresponds to side a of triangle A}$,

$\text{Sides of " Delta B } a r e 14 , \left(\frac{14}{48}\right) \cdot 36 , \left(\frac{14}{48}\right) \cdot 54 = 14 , \frac{28}{3} , \frac{63}{4}$

$\text{When side 14 of triangle B corresponds to side b of triangle B}$,

$\text{Sides of " Delta B } a r e \left(\frac{14}{36}\right) \cdot 48 , 14 , \left(\frac{14}{36}\right) \cdot 54 = \frac{56}{3} , 14 , 21$

$\text{When side 14 of triangle B corresponds to side c of triangle B}$,

$\text{Sides of " Delta B } a r e \left(\frac{14}{54}\right) \cdot 48 , \left(\frac{14}{54}\right) \cdot 36 , 14 = \frac{112}{9} \frac{28}{3} , 14$