# Triangle A has sides of lengths 15 , 9 , and 12 . Triangle B is similar to triangle A and has a side of length 24 . What are the possible lengths of the other two sides of triangle B?

Mar 11, 2016

30,18

#### Explanation:

sides of triangle A are 15,9,12
${15}^{2} = 225$,${9}^{2} = 81$,${12}^{2} = 144$
It is seen that square of the greatest side (225) is equal to the sum of square of other two sides (81+144) . Hence triangle A is right angled one.
Similar triangle B must also be right angled. One of its sides is 24.
If this side is considered as corresponding side with the side of 12 unit length of triangle A then other two sides of triangle B should have possible length 30(=15x2) and 18 (9x2)

Mar 11, 2016

(24,72/5,96/5 ) , (40,24,32) , (30,18,24)

#### Explanation:

Since the triangles are similar then the ratios of corresponding sides are equal.

Name the 3 sides of triangle B , a , b and c , corresponding to the sides 15 , 9 and 12 in triangle A.
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If side a = 24 then ratio of corresponding sides =$\frac{24}{15} = \frac{8}{5}$

hence b = $9 \times \frac{8}{5} = \frac{72}{5} \text{ and } c = 12 \times \frac{8}{5} = \frac{96}{5}$

The 3 sides in B $= \left(24 , \frac{72}{5} , \frac{96}{5}\right)$
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If side b = 24 then ratio of corresponding sides $= \frac{24}{9} = \frac{8}{3}$

hence a = $15 \times \frac{8}{3} = 40 \text{ and } c = 12 \times \frac{8}{3} = 32$

The 3 sides in B = (40 . 24 , 32 )
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If side c = 24 then ratio of corresponding sides $= \frac{24}{12} = 2$

hence a $= 15 \times 2 = 30 \text{ and } b = 9 \times 2 = 18$

The 3 sides in B = ( 30 , 18 , 24 )
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