Question

The sides of the triangular ground are 22m ,120m find the area and cost Of levelling The ground at the rate of rupees 20 per m²

Answer 1

$\large\bf\underline{Correct\: Question:-}$

The sides of the triangular ground are 22m ,120m and 122m .find the area and cost Of levelling The ground at the rate of rupees 20 per m²

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$\large\bf\underline{Given:-}$

• Side's of triangle = 120m, 22m, 122m
• cost of levelling the ground = 20 per m²

$\large\bf\underline {To \: find:-}$

• Total cost of levelling the ground

$\huge\bf\underline{Solution:-}$

Sides are 22m, 120m, 122m.

The Given sides are of different lengths.

Area of triangle by Heron's Formula

$\underline {\boxed{ \bf \: \sqrt{s(s-a)(s-b)(s-c)}}}$

$\bf \: s = \frac{a + b + c}{2}$

where,

a ,b and c are the sides of triangle.

• a = 22m
• b = 120m
• c = 122m

$\leadsto \rm \: s = \frac{22 + 120 + 122}{2} \\ \\ \leadsto \rm \: s = \frac{264}{2} \\ \\ \leadsto \rm \: s =132m$

Now, Area of Triangle:-

$\leadsto \rm \: \sqrt{132(132 - 22)(132 - 120)(132 - 122)} \\ \\ \leadsto \rm \: \sqrt{132(110)(12)(10)} \\ \\ \leadsto \rm \: \sqrt{132 \times 13200} \\ \\ \leadsto \rm \: \sqrt{1742400} \\ \\ \rm \: area \: of \: triangle = 1320 {m}^{2}$

Now, Cost of levelling 1m² = Rs 20

Cost of levelling whole field = 20 × 1320

Cost of levelling whole field = Rs 26400

Answer 2

$\sf Correct\: Question :$

The sides of the triangular ground are 22m,120m and 122m find the area and cost of levelling The ground at the rate of rupees 20 per m².

⠀⠀⠀$\rule{160}{1}$

$\sf Answer :$

✩ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,8)\linethickness{0.5mm}\qbezier(1,.5)(2,1)(4,2)\qbezier(4,2)(2,3)(2,3)\qbezier(2,3)(2,3)(1,0.5)\put(.7, .3){ C }\put(4.05, 1.9){ B }\put(1.7, 2.95){ A }\put(3.2, 2.5){\sf{22 m}}\put(0.7,1.7){\sf{120 m}}\put(2.7, 1.05){\sf{122 m}}\end{picture}$

⠀

☢ $\underline{\textsf{Semi - Perimeter of the Triangle :}}$

$:\implies\sf Semi \:Perimeter=\dfrac{Sum\:of\:Sides}{2}\\\\\\:\implies\sf s = \dfrac{a + b + c}{2}\\\\\\:\implies\sf s = \dfrac{20 + 120 + 122}{2}\\\\\\:\implies\sf s = \dfrac{264}{2}\\\\\\:\implies\sf s =132$

$\rule{120}{0.8}$

☢ $\underline{\textsf{Price of Levelling of the Ground :}}$

$\dashrightarrow\sf\:\:Cost=Area \times Rate\\\\\\\dashrightarrow\sf\:\:Cost=\sqrt{s(s-a)(s-b)(s-c)} \times Rate\\\\\\\dashrightarrow\sf\:\:Cost=\sqrt{132(132-22)(132-120)(132-122)} \times 20\\\\\\\dashrightarrow\sf\:\:Cost = \sqrt{132 \times 110 \times 12 \times 10} \times 20\\\\\\\dashrightarrow\sf\:\:Cost = \sqrt{132 \times 132 \times 100} \times 20\\\\\\\dashrightarrow\sf\:\:Cost = 132 \times 10 \times 20\\\\\\\dashrightarrow\:\:\underline{\boxed{\textsf{Cost = Rs. 26,400}}}$

⠀

$\therefore\:\underline{\textsf{Cost of levelling of ground is \textbf{Rs. 26,400}}}.$