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?

Mar 11, 2016

$\max = 106.67 s q u n i t$ and$\min = 78.37 s q u n i t$

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
${\Delta}_{B} / {\Delta}_{A} = {16}^{2} / {6}^{2}$
${\Delta}_{B} = {16}^{2} / {6}^{2} \times 15 = 106.67 s q u n i t$ Maximum

Possibility -2
when side of length 16 of B is the corresponding side of length 7 of triangle A then
${\Delta}_{B} / {\Delta}_{A} = {16}^{2} / {7}^{2}$
${\Delta}_{B} = {16}^{2} / {7}^{2} \times 15 = 78.37 s q u n i t$ Minimum