# Triangle A has sides of lengths 18 ,3 3 , and 21 . Triangle B is similar to triangle A and has a side of length 14 . What are the possible lengths of the other two sides of triangle B?

Aug 14, 2018

77/3\ &\ 49/3

#### Explanation:

When two triangles are similar, the ratios of the lengths of their corresponding sides are equal.

So,

$\text{Side length of first triangle"/"Side length of second triangle} = \frac{18}{14} = \frac{33}{x} = \frac{21}{y}$

Possible lengths of other two sides are:

x = 33 × 14/18 = 77/3

y = 21 × 14/18 = 49/3

Aug 14, 2018

Possible length of other two sides of triangle B are
$\left(25.67 , 16.33\right) , \left(7.64 , 8.91\right) , \left(12 , 22\right)$ units

#### Explanation:

Triangle A sides are $18 , 33 , 21$

Assuming side $a = 14$ of triangle B is similar to side $18$ of

triangle $A \therefore \frac{18}{14} = \frac{33}{b} \therefore b = \frac{33 \cdot 14}{18} = 25 \frac{2}{3} \approx 25.67$ and

$\frac{18}{14} = \frac{21}{c} \therefore c = = \frac{21 \cdot 14}{18} = 16 \frac{1}{3} \approx 16.33$

Possible length of other two sides of triangle B are

$25.67 , 16.33$ units

Assuming side $b = 14$ of triangle B is similar to side $33$ of

triangle $A \therefore \frac{33}{14} = \frac{18}{a} \therefore a = \frac{18 \cdot 14}{33} = 7 \frac{7}{11} \approx 7.64$ and

$\frac{33}{14} = \frac{21}{c} \therefore c = = \frac{21 \cdot 14}{33} = 8 \frac{10}{11} \approx 8.91$

Possible length of other two sides of triangle B are

$7.64 , 8.91$units

Assuming side $c = 14$ of triangle B is similar to side $21$ of

triangle $A \therefore \frac{21}{14} = \frac{18}{a} \therefore a = \frac{18 \cdot 14}{21} = 12$ and

$\frac{21}{14} = \frac{33}{b} \therefore b = \frac{33 \cdot 14}{21} = 22$

Possible length of other two sides of triangle B are

$12 , 22$ units. Therefore , possible length of other two sides

of triangle B are $\left(25.67 , 16.33\right) , \left(7.64 , 8.91\right) , \left(12 , 22\right)$units [Ans]