Question

e two sides of a triangle are 8 cm and 11 cm and the perimeter is 32 cm . Find the third side and the area of the triangle .

(2 Points)​

Answer 1

8√30 cm² = 43.82 cm²

Step-by-step explanation:

$let \: 3rd \: side \: = \: x \: cm \\ perimeter = 32 \: cm \\ 8 + 11 + x = 32 \\ 19 + x = 32 \: \\ x = 32 - 19 \\ x = 13 \\ 3rd \: side \: = 13 \: cm \\ semi \: perimeter \: = \frac{32}{2}cm \\ s = 16 \: cm \\ a = 8 \: cm \: \\ b \:= \: 11 \: cm \: \\ c = 13cm \\ by \: herons \: formula \\ area = \sqrt{s \times s - a \times s - b \times s - c} \\ = \sqrt{16 \times 16 - 8 \times 16 - 11 \times 16 - 13} \\ = \sqrt{16 \times 8 \times 5 \times 3} \\ = 8 \sqrt{2 \times 5 \times 3} \\ = 8 \sqrt{30} = 43.82 cm² \\ area \: of \: triangle \: = 8 \sqrt{30} \: {cm}^{2} = 43.82 cm²$