Triangle A has sides of lengths #32 #, #24 #, and #20 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #32    #, #24    #, and #20     #. Triangle B is similar to triangle A and has a side with a length of #16     #. What are the possible lengths of the other two sides of triangle B?

Sophia Alfred · Accepted Answer

Case (1) 16, 19.2, 25.6
Case (2) 16, 13.3333, 21.3333
Case (3) 16, 10, 12

Triangles A & B are similar. Case (1) #:.16/20=b/24=c/32# #b=(16*24)/20= 19.2# #c=(16*32)/20= 25.6# Possible lengths of other two sides of triangle B are #16, 19.2, 25.6# Case (2) #:.16/24=b/20=c/32# #b=(16*20)/24=13.3333# #c=(16 * 32)/24=21.3333# Possible lengths of other two sides of triangle B are #16, 13.3333, 21.3333# Case (3) #:.16 /32=b/20=c/24# #b=(16*20)/32=10# #c=(16*24)/32=12# Possible lengths of other two sides of triangle B are #16, 10, 12#

Evelyn Arboleda · Answer

undefined Since triangles A and B are similar, their corresponding sides are proportional. Let $ x $ represent the length of the side in triangle B that corresponds to the side with a length of 32 in triangle A.

Using the ratio of corresponding sides:

$$
\frac{{\text{{length of corresponding side in triangle B}}}}{{\text{{length of corresponding side in triangle A}}}} = \frac{{\text{{length of given side in triangle B}}}}{{\text{{length of given side in triangle A}}}}
$$

we have:

$$
\frac{x}{32} = \frac{16}{32}
$$

Solving for $ x $, we get:

$$
x = 8
$$

So, the length of the side in triangle B that corresponds to the side with a length of 24 in triangle A is $ 8 $.

Similarly, the length of the side in triangle B that corresponds to the side with a length of 20 in triangle A is also $ \frac{16}{32} \times 20 = 10 $.

Therefore, the possible lengths of the other two sides of triangle B are $ 8 $ and $ 10 $.