Question

A triangle shaped land has the sides in the ratio 3:5:7 . If its perimeter is 300 meter . What will the area of the land

Answer 1

EXPLANATION.

=> A triangular shaped land has the sides in the

ratio = 3:5:7

=> it's perimeter = 300 m.

To find area of the land.

$\sf : \implies \: let \: the \: sides \: of \: triangle \: = 3x,5x,7x \\ \\ \sf : \implies \: 3x + 5x + 7x = 300 \\ \\ \sf : \implies \: 15x = 300 \\ \\ \sf : \implies \: x \: = 20 \:$

$\sf : \implies \: their \: sides \: are \: \\ \\ \sf : \implies \: 3x = 3 \times 20 = 60 \\ \\ \sf : \implies \: 5x = 5 \times 20 = 100 \\ \\ \sf : \implies \: 7x = 7 \times 20 = 140$

$\sf : \implies \: by \: using \: herons \: formula \: \\ \\\sf : \implies \: s \: = \frac{a + b + c}{2} \\ \\ \sf : \implies \: s \: = \frac{60 + 100 + 140}{2} = \frac{300}{2} = 150 \: m$

$\sf : \implies \: herons \: formula \: \\ \\ \sf : \implies \: \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sf : \implies \: \sqrt{150(150 - 60)(150 - 100)(150 - 140)} \\ \\ \sf : \implies \: \sqrt{150 \times 90 \times 50 \times 10} \\ \\ \sf : \implies \: \sqrt{6750000} \\ \\ \sf : \implies \: 1500 \sqrt{3} m {}^{2}$

$\sf : \implies \: \green{{ \underline{area \: of \: land \: = 1500 \sqrt{3} {m}^{2} }}}$