Question

triangle lmn has sides measuring 7 meters and 6 meters and a perimeter of 16 meters. herons formula: area = \sqrt{s(s - a)(s - b)(s - c)} what is the area of triangle lmn? round to the nearest square meter. 34 square meters 3 square meters 9 square meters 28 square meters

Explanation:

Step1: Find the third - side length

Let the sides be \(a = 7\), \(b = 6\), and the perimeter \(P=a + b + c=16\). Then \(c=P-(a + b)=16-(7 + 6)=3\).

Step2: Calculate the semi - perimeter \(s\)

The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{7+6 + 3}{2}=\frac{16}{2}=8\).

Step3: Apply Heron's formula

Area \(A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{8(8 - 7)(8 - 6)(8 - 3)}=\sqrt{8\times1\times2\times5}=\sqrt{80}\approx9\).

Answer:

9 square meters