Question

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?

Answer 1

`77/3\ &\ 49/3`

Explanation:

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

So,

`"Side length of first triangle"/"Side length of second triangle" = 18/14 = 33/x = 21/y`

Possible lengths of other two sides are:

`x = 33 × 14/18 = 77/3`

`y = 21 × 14/18 = 49/3`

Answer 2

Possible length of other two sides of triangle B are
`(25.67,16.33), (7.64,8.91) , (12,22)` units

Explanation:

Triangle A sides are `18 ,33 , 21`

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

triangle `A :. 18/14=33/b :. b=(33*14)/18=25 2/3~~25.67` and

`18/14=21/c :. c==(21*14)/18=16 1/3~~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 :. 33/14=18/a :. a=(18*14)/33=7 7/11~~7.64` and

`33/14=21/c :. c==(21*14)/33=8 10/11~~ 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 :. 21/14=18/a :. a=(18*14)/21=12` and

`21/14=33/b :. b=(33*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 `(25.67,16.33), (7.64,8.91) , (12,22)`units [Ans]