Question

find the cost leveling a ground in the form a traingle with sides 16cm 12cm 20 cm at rs 4 per sq meter​

Answer 1

Correct Question:

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• Find the cost leveling a ground in the form a traingle with sides 16 m, 12 m, 20 m at rs 4 per sq. meter.

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☯ Let sides of triangle be a, b and c.

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$\sf \therefore\;Sides_{\;\triangle} \begin{cases} & \sf{a = \bf{16\;cm}} \\ & \sf{b = \bf{12\;cm}} \\ & \sf{c = \bf{20\;cm}} \end{cases}$

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$\underline{\bigstar\:\boldsymbol{Using\: Heron's\:Formula\::}}$

$\star\;\sf s = semi - perimeter\\ \\ :\implies\sf s = \dfrac{a + b + c}{2}\\ \\ :\implies\sf s = \dfrac{16 + 12 + 20}{2}\\ \\ :\implies\sf s = \cancel{ \dfrac{48}{2}}\\ \\ :\implies{\boxed{\red{\sf{s = 24}}}}\;\bigstar$

Now, Area of triangle,

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$\star\;{\boxed{\sf{\purple{Area_{\;\triangle} = \sqrt{s(s - a)(s - b)(s - c)}}}}}$

$:\implies\sf \sqrt{24(24 - 16)(24 - 12)(24 - 20)}\\ \\ :\implies\sf \sqrt{24 \times 8 \times 12 \times 4}\\ \\ :\implies\sf \sqrt{9216}\\ \\ :\implies{\boxed{\sf{\pink{96\; m^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\;Area\;of\;of\;ground\;is\; \bf{96\;m^2}.}}}$

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Given that,

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Cost of per meter square = 4 Rs.

$\rightarrow$ Cost of 96 m² = 4 × 96 = 384 Rs.

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$\therefore\;{\underline{\sf{Hence,\;Cost\;of\;of\;leveling\;ground\;is\; \bf{384\;Rs}.}}}$