Triangle A has sides of lengths #60 #, #42 #, and #54 #. 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 #60    #, #42    #, and #54     #. 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?

Claire Akin · Accepted Answer

Possible lengths of two triangles are

Case 1 : #color(green)(A (42, 54, 60) & B (7. 8.2727, 10))#

Case 2 : #color(brown)(A (42, 54, 60) & B (5.4444, 7, 7.7778))#

Case 3 :# color(blue)( A (42, 54, 60) & B (4.9, 6.3, 7))#

Aurora Ayala · Answer

undefined Using the concept of similarity between triangles, the ratios of corresponding sides in similar triangles are equal.

For triangle $ A $, the side lengths are given as 60, 42, and 54.

Let's denote the sides of triangle $ B $ as $ x $ and $ y $. Since triangle $ B $ is similar to triangle $ A $, the ratio of corresponding sides must be equal.

The ratio of the corresponding sides between $ A $ and $ B $ is as follows:

$$
\frac{x}{60} = \frac{7}{42} = \frac{y}{54}
$$

From the given ratios, we can solve for $ x $ and $ y $:

$$
x = \frac{7}{42} \times 60
$$
$$
y = \frac{7}{42} \times 54
$$

Solving these equations gives the possible lengths of the sides of triangle $ B $:

$$
x = 10
$$
$$
y = 9
$$

So, the possible lengths of the other two sides of triangle $ B $ are 10 and 9.