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. 9 square meters 34 square meters 28 square meters 3 square meters

Explanation:

Step1: Find the missing side

Let the sides be $a=7$, $b=6$, $c=?$
Perimeter $P = a+b+c = 16$
$c = 16 - 7 - 6 = 3$

Step2: Calculate semi-perimeter $s$

$s = \frac{P}{2} = \frac{16}{2} = 8$

Step3: Apply Heron's formula

$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$
$\text{Area} = \sqrt{8(8-7)(8-6)(8-3)}$
$\text{Area} = \sqrt{8\times1\times2\times5} = \sqrt{80} \approx 8.94$

Step4: Round to nearest square meter

$\approx 9$

Answer:

9 square meters