Question

Triangle A has an area of `5` and two sides of lengths `6` and `3`. Triangle B is similar to triangle A and has a side with a length of `9`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Maximum area of triangle B = 45

Minimum area of triangle B = 11.25

Explanation:

Triangle A sides 6,3 & area 5.

Triangle B side 9

For maximum area of triangle B : side 9 will be proportional to side 3 of triangle A.
Then the side ratio is 9:3. Therefore, areas will be in the ratio of
`9^2 : 3^3 = 81/9 = 9`
`:.` Maximum Area of triangle `B = 5 * 9 = 45`

Similarly, for minimum area of triangle B,
side 9 of triangle B will correspond to side 6 of triangle A.
Sides ratio `= 9 : 6`and areas ratio `= 9^2:6^2 = 9:4 = 2.25`
`:.` Minimum area of triangle `B = 5*2.25 = 11.25`