Question

Triangle A has an area of `25` and two sides of lengths `9` and `6`. Triangle B is similar to triangle A and has a side of length `8`. What are the maximum and minimum possible areas of triangle B?

Answer 1

Area ob B could be 19.75 or 44.44

Explanation:

The areas of similar figures are in the same ratio as the ratio of the squares of the sides.
In this case we do not know whether triangle b is bigger or smaller than triangle A, so we will have to consider both possibilities.

If A is bigger:`" " 9^2/8^2 = 25/x " "rArr x = (8^2 xx 25)/9^2`

Area = `19.75`

If A is smaller:`" " 6^2/8^2 = 25/x " "rArr x = (8^2 xx 25)/6^2`

Area = `44.44`