Triangle A has sides of lengths #24 #, #28 #, and #16 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #24    #, #28    #, and #16     #. Triangle B is similar to triangle A and has a side of length #7     #. What are the possible lengths of the other two sides of triangle B?

Autumn Armstrong · Accepted Answer

Three sets of possible lengths are
1) # 7, 49/6, 14/3#
2) # 7, 6, 4#
3) #7, 21/2, 49/4# If two triangles are similar, their sides are on the same proportion. #A/a = B/b = C/c# Case 1. #24/7 = 28/b = 16/c# #b = (28*7)/24 = 49/6# #c = (16*7)/24 = 14/3# Case 2. #28/7 = 24/b = 16/c# #b = 6, c = 4# Case 3. #16/7 =24/b = 28/c# #b 21/2, c = 49/4#

Sophia Alfred · Answer

undefined To find the possible lengths of the other two sides of triangle B, we need to use the properties of similar triangles. Since triangle B is similar to triangle A, the corresponding sides are in proportion.

Let's denote the corresponding sides of triangle A and triangle B as follows:
- Side of length 24 in triangle A corresponds to a side of length x in triangle B.
- Side of length 28 in triangle A corresponds to a side of length y in triangle B.
- Side of length 16 in triangle A corresponds to a side of length 7 in triangle B.

We can set up a proportion based on the ratios of corresponding sides:

$$ \frac{x}{24} = \frac{7}{16} $$
$$ \frac{y}{28} = \frac{7}{16} $$

Solving for x and y, we get:
$$ x = \frac{7}{16} \times 24 = 10.5 $$
$$ y = \frac{7}{16} \times 28 = 12.25 $$

So, the possible lengths of the other two sides of triangle B are approximately 10.5 and 12.25.