Question

Triangle A has an area of `15` and two sides of lengths `6` and `7`. Triangle B is similar to triangle A and has a side with a length of `16`. What are the maximum and minimum possible areas of triangle B?

Answer 1

`max=106.67squnit` and`min=78.37squnit`

Explanation:

The area of 1st triangle,A `Delta_A=15`
and length of its sides are 7 and 6
Length of one side of 2nd triangle is=16
let the area of 2nd triangle,B =`Delta_B`
We will use the relation:
The ratio of the areas of similar triangles is equal to the ratio of the squares of their corresponding sides.

Possibility -1
when side of length 16 of B is the corresponding side of length 6 of triangle A then
`Delta_B/Delta_A=16^2/6^2`
`Delta_B=16^2/6^2xx15=106.67squnit` Maximum

Possibility -2
when side of length 16 of B is the corresponding side of length 7 of triangle A then
`Delta_B/Delta_A=16^2/7^2`
`Delta_B=16^2/7^2xx15=78.37squnit` Minimum