Triangle A has sides of lengths #48 ,24 #, and #54 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #48     ,24   #, and #54  #. Triangle B is similar to triangle A and has a side of length #5   #. What are the possible lengths of the other two sides of triangle B?

Noah Atkinson · Accepted Answer

several possibilities. See explanation.

We know, if #a,b,c# represent the sides of a triangle, then a similar triangle will have side given by #a',b',c'# that follows: #a/(a')=b/(b')=c/(c')# Now, let #a=48," " b=24 " and "c=54# There are three possibilities: so, #b' = 24xx5/48 = 5/2# and, #c' = 54xx5/48 = 45/8# so, #a' = 48xx5/24 = 10# and, #c' = 54xx5/24 = 45/4# so, #a' = 48xx5/54 = 40/9# and, #b' = 24xx5/54 = 20/9#

Avery Allen · 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 of the two triangles are proportional.

Let's denote the lengths of the other two sides of triangle B as $ x $ and $ y $.

By the property of similar triangles, we can set up the following proportion:

$$
\frac{x}{48} = \frac{5}{24}
$$

Solving this proportion for $ x $, we get:

$$
x = \frac{5 \times 48}{24} = 10
$$

Similarly, we can set up another proportion using the lengths of the longest sides of the triangles:

$$
\frac{y}{54} = \frac{5}{24}
$$

Solving this proportion for $ y $, we get:

$$
y = \frac{5 \times 54}{24} = \frac{135}{4} = 33.75
$$

Therefore, the possible lengths of the other two sides of triangle B are 10 and 33.75.