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Triangle LMN has sides measuring 7 meters and 6 meters and a perimeter of 16 meters.

What is the area of triangle LMN? Round to the nearest square meter.
3 square meters
9 square meters
28 square meters
34 square meters

User Ataulm
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2 Answers

2 votes
the answer is 9 square meters
User Notconfusing
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Answer: The area of the triangle is 9 m².

Step-by-step explanation: Given that the measures of two sides of triangle LMN are 7 meters and 6 meters.

We are to find the area of the triangle if its perimeter is 16 meters.

Let, a, b and c represents the lengths of three sides of a triangle.

Then, the area of the triangle will be


A=√(s(s-a)(s-b)(s-c)),~~~\textup{where }s=(a+b+c)/(2).

In ΔLMN,

a = 7 m and b = 6 meters.

The perimeter of ΔLMN is 16 meters. So, we have


a+b+c=16\\\\\Rightarrow 7+6+c=16\\\\\Rightarrow 13+c=16\\\\\Rightarrow c=3.

This implies that


s=(a+b+c)/(2)=(7+6+3)/(2)=8.

Therefore, the area of ΔLMN is


A\\\\=√(s(s-a)(s-b)(s-c))\\\\=√(8*(8-7)*(8-6)*(8-3)))\\\\=√(8* 1* 2* 5)\\\\=√(80)\\\\=8.9442\sim 9~\textup{m}^2.

Thus, the area of the triangle is 9 m².

User Twiz
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