Question

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

Answer 1

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

$A=\sqrt{s(s-a)(s-b)(s-c)},~~~\textup{where }s=\dfrac{a+b+c}{2}.$

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

$s=\dfrac{a+b+c}{2}=\dfrac{7+6+3}{2}=8.$

Therefore, the area of ΔLMN is

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

Thus, the area of the triangle is 9 m².

Answer 2

The answer is 9 square meters