Question

If the lenght of sides of tringle is 30,40,50 find the area solve

Answer 1

$\textbf{Hey there!}\\\\\text{Thank you for your question!}\\\\Given,\\\textbf{\underline{Lengths of sides of}} \ \triangle: \\a = 30 \ unit\\b = 40 \ unit \\ c = 50 \ unit\\\\\textbf{\underline{Find semi perimeter of triangle :}} \\\\\boxed{\boxed{s = \frac{a+b+c}{2}}}\\\\s = \frac{30 + 40 + 50}{2}\\\\s = \frac{120}{2}\\\\\boxed{\bold{s = 60}}$

$\\\\\textbf{\underline{Finding area using Heron's Formula:}}\\Area = \sqrt{s(s-a)(s-b)(s-c)}\\~~~~~~~~=\sqrt{60(60-30)(60-40)(60-50)}\\~~~~~~~~=\sqrt{60 \times 30 \times 20 \times 10}\\~~~~~~~~=\sqrt{2 \times 30\times 30 \times 2 \times 10 \times 10}\\~~~~~~~~=\sqrt{2 \times 2 \times 30 \times 30\times 10 \times 10}\\~~~~~~~~=2 \times 30 \times 10 \\~~~~~~~~= 600\ sq. \ unit$

$\text{Hence, the required area is 600 sq. unit.}$