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?

Question

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?

Sophia Alfred · Accepted Answer

#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# #"in " Delta A : a = 48, b = 36, c = 54, " in " Delta B : " one side " = 14# #"When side 14 of triangle B corresponds to side a of triangle A"#, #"Sides of " Delta B " are 14, (14/48)*36, (14/48)*54 = 14, 28/3, 63/4# #"When side 14 of triangle B corresponds to side b of triangle B"#, #"Sides of " Delta B " are (14/36)*48, 14, (14/36)*54 = 56/3, 14, 21# #"When side 14 of triangle B corresponds to side c of triangle B"#, #"Sides of " Delta B " are (14/54)*48, (14/54)*36, 14 =112/9 28/3, 14#

Aaliyah Anderson · Answer

undefined Since triangles $A$ and $B$ are similar, their corresponding sides are proportional.

Let $x$ and $y$ be the lengths of the other two sides of triangle $B$. Then we have the following proportion:

$$
\frac{x}{48} = \frac{14}{54}
$$

Solving this proportion for $x$, we get:

$$
x = \frac{14 \times 48}{54} = \frac{4 \times 48}{3} = \frac{4}{3} \times 48 = 64
$$

Similarly, for $y$, we have:

$$
\frac{y}{36} = \frac{14}{54}
$$

Solving this proportion for $y$, we get:

$$
y = \frac{14 \times 36}{54} = \frac{2 \times 36}{3} = \frac{2}{3} \times 36 = 24
$$

Therefore, the possible lengths of the other two sides of triangle $B$ are $64$ and $24$.