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

Jun 10, 2016

$10 \mathmr{and} 4.9$

#### Explanation:

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Let two triangles $A \mathmr{and} B$ be similar. $\Delta A$ is $O P Q$ and has sides $60 , 42 \mathmr{and} 60$. Since two sides are equal to each other it is an isosceles triangle.
and $\Delta B$ is $L M N$ has one side$= 7$.
By properties of Similar Triangles

1. Corresponding angles are equal and
2. Corresponding sides are all in the same proportion.

It follows that $\Delta B$ must also be an isosceles triangle.

There are two possibilities
(a) Base of $\Delta B$ is $= 7$.
From proportionality
${\text{Base"_A/"Base"_B="Leg"_A/"Leg}}_{B}$ .....(1)
Inserting given values
$\frac{42}{7} = \frac{60}{\text{Leg}} _ B$
$\implies {\text{Leg}}_{B} = 60 \times \frac{7}{42}$
$\implies {\text{Leg}}_{B} = 10$

(b) Leg of $\Delta B$ is $= 7$.
From equation (1)
$\frac{42}{\text{Base}} _ B = \frac{60}{7}$
${\text{Base}}_{B} = 42 \times \frac{7}{60}$
${\text{Base}}_{B} = 4.9$