# 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?

##### 2 Answers

30,18

#### Explanation:

sides of triangle A are 15,9,12

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)

(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 =#24/15 = 8/5# hence b =

# 9xx8/5= 72/5 " and " c = 12xx8/5 = 96/5# The 3 sides in B

#= (24 , 72/5 , 96/5 )#

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If side b = 24 then ratio of corresponding sides#= 24/9 = 8/3# hence a =

# 15xx8/3 = 40" and " c = 12xx8/3 = 32# The 3 sides in B = (40 . 24 , 32 )

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If side c = 24 then ratio of corresponding sides#= 24/12 = 2# hence a

#= 15xx2 = 30" and " b = 9xx2 = 18# The 3 sides in B = ( 30 , 18 , 24 )

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