Question

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

Answer 1

the answer is 9 square meters

Answer 2

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.