Triangle A has sides of lengths #18 #, #12 #, and #21 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #18    #, #12    #, and #21     #. Triangle B is similar to triangle A and has a side of length #24     #. What are the possible lengths of the other two sides of triangle B?

Avery Allen · Accepted Answer

#Delta (24, a, b)#

#Delta (24, c, d)#

#Delta (24, e, f)# #{18/24 = 12/a = 21/b} or # #{18/c = 12/24 = 21/d} or {18/e = 12/f = 21/24}# #a = 24 * 12/18 = 16# #b = 24 * 21/18 = 28# #c = 18 * 24/12 = 36# #d = 24 * 21/12 = 42# #e = 18 * 24/21 = 144/7# #f = 12 * 24/21 = 96/7#

Theodore Abad · Answer

undefined Using the property of similar triangles, the ratio of corresponding sides in similar triangles is constant.

For Triangle A, let's denote the sides as $ a = 18 $, $ b = 12 $, and $ c = 21 $.

Triangle B is similar to Triangle A, and it has a side of length 24. Let's denote the corresponding sides in Triangle B as $ x $ and $ y $.

We can set up proportions using the ratios of corresponding sides:

$$ \frac{x}{a} = \frac{24}{18} $$
$$ \frac{y}{b} = \frac{24}{12} $$

Solving for $ x $ and $ y $ will give us the possible lengths of the other two sides of Triangle B:

$$ x = \frac{24}{18} \times a $$
$$ y = \frac{24}{12} \times b $$

$$ x = \frac{4}{3} \times 18 $$
$$ y = 2 \times 12 $$

$$ x = 24 $$
$$ y = 24 $$

So, the possible lengths of the other two sides of Triangle B are both 24.