# Triangle A has sides of lengths 1 3 ,1 4, and 11 . Triangle B is similar to triangle A and has a side of length 4 . What are the possible lengths of the other two sides of triangle B?

Given Triangle A: $13 , 14 , 11$
Triangle B: $4 , \frac{56}{13} , \frac{44}{13}$
Triangle B: $\frac{26}{7} , 4 , \frac{22}{7}$
Triangle B: $\frac{52}{11} , \frac{56}{11} , 4$

#### Explanation:

Let triangle B have sides x, y, z then, use ratio and proportion to find the other sides.
If the first side of triangle B is x=4, find y, z

solve for y:

$\frac{y}{14} = \frac{4}{13}$

$y = 14 \cdot \frac{4}{13}$

$y = \frac{56}{13}$
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solve for z:
$\frac{z}{11} = \frac{4}{13}$

$z = 11 \cdot \frac{4}{13}$
$z = \frac{44}{13}$
Triangle B: $4 , \frac{56}{13} , \frac{44}{13}$

the rest are the same for the other triangle B

if the second side of triangle B is y=4, find x and z

solve for x:
$\frac{x}{13} = \frac{4}{14}$
$x = 13 \cdot \frac{4}{14}$
$x = \frac{26}{7}$

solve for z:
$\frac{z}{11} = \frac{4}{14}$
$z = 11 \cdot \frac{4}{14}$
$z = \frac{22}{7}$

Triangle B:$\frac{26}{7} , 4 , \frac{22}{7}$
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If the third side of triangle B is z=4, find x and y
$\frac{x}{13} = \frac{4}{11}$
$x = 13 \cdot \frac{4}{11}$
$x = \frac{52}{11}$

solve for y:

$\frac{y}{14} = \frac{4}{11}$

$y = 14 \cdot \frac{4}{11}$
$y = \frac{56}{11}$

Triangle B:$\frac{52}{11} , \frac{56}{11} , 4$

God bless....I hope the explanation is useful.