Question

Triangle A has sides of lengths `7 ,4`, and `8`. Triangle B is similar to triangle A and has a side of length `9`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible lengths of the triangle B are

Case (1)
`9, 15.75, 18`

Case (2)
`9, 5.14, 10.29`

Case (3)
`9, 4.5, 7.875`

Explanation:

Triangles A & B are similar.
Case (1)
`:.9/4=b/7=c/8`
`b=(9*7)/4= 15.75`
`c=(9*8)/4= 18`

Possible lengths of other two sides of triangle B are
`9, 15.75, 18`

Case (2)
`:.9/7=b/4=c/8`
`b=(9*4)/7=5.14`
`c=(9*8)/7=10.29`

Possible lengths of other two sides of triangle B are
`9, 5.14, 10.29`

Case (3)
`:.9/8=b/4=c/7`
`b=(9*4)/8=4.5`
`c=(9*7)/8=7.875`

Possible lengths of other two sides of triangle B are
`9, 4.5, 7.875`