Question

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?

Answer 1

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)

Answer 2

(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 =`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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