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?

1 Answer
P dilip_k
Mar 11, 2016

#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

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