Triangle A has sides of lengths #36 #, #42 #, and #48 #. 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 #36    #, #42    #, and #48     #. 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?

Sadie Adams · Accepted Answer

Triangle B has sides of lengths 6, 7, and 8.

The first thing is to compute 42/7. Now we have 6. 36/6 = 6 48/6=8, We will get 6 and 8 as lengths of triangle B. Triangle B has sides of lengths 6, 7, and 8.

Evelyn Arboleda · Answer

undefined To find the possible lengths of the other two sides of triangle B, which is similar to triangle A, you can use the property of similar triangles. Since triangle B is similar to triangle A, their corresponding sides are proportional.

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

Using the property of similar triangles, we have:

$$ \frac{x}{36} = \frac{y}{42} = \frac{7}{48} $$

From the given information, we can solve for $ x $ and $ y $.

1. Solve for $ x $:

$$ \frac{x}{36} = \frac{7}{48} $$

$$ x = \frac{7 \times 36}{48} $$

$$ x = \frac{7 \times 3}{4} $$

$$ x = \frac{21}{4} $$

2. Solve for $ y $:

$$ \frac{y}{42} = \frac{7}{48} $$

$$ y = \frac{7 \times 42}{48} $$

$$ y = \frac{7 \times 7}{8} $$

$$ y = \frac{49}{8} $$

So, the possible lengths of the other two sides of triangle B are:

$$ x = \frac{21}{4} $$
$$ y = \frac{49}{8} $$