Question

Triangle A has an area of `27` and two sides of lengths `8` and `6`. Triangle B is similar to triangle A and has a side with a length of `8`. What are the maximum and minimum possible areas of triangle B?

Answer 1

maximum possible area of triangle B `=48` &

minimum possible area of triangle B `=27`

Explanation:

Given area of triangle A is

`\Delta_A=27`

Now, for maximum area `\Delta_B` of triangle B, let the given side `8` be corresponding to the smaller side `6` of triangle A.

By the property of similar triangles that the ratio of areas of two similar triangles is equal to the square of ratio of corresponding sides then we have

`\frac{\Delta_B}{\Delta_A}=(8/6)^2`

`\frac{\Delta_B}{27}=16/9`

`\Delta_B=16\times 3`

`=48`

Now, for minimum area `\Delta_B` of triangle B, let the given side `8` be corresponding to the greater side `8` of triangle A.

The ratio of areas of similar triangles A & B is given as

`\frac{\Delta_B}{\Delta_A}=(8/8)^2`

`\frac{\Delta_B}{27}=1`

`\Delta_B=27`

Hence, the maximum possible area of triangle B `=48` &

the minimum possible area of triangle B `=27`