Question

plzzzzzz help me...​

Answer 1

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

If a, b, c are the sides of a triangle and s is the Semi-perimeter, then its area is given by :

Using Heron's Formula :

$\bigstar \boxed{ \sf \: \triangle \: = \sqrt{s(s - a)(s - b)(s - c)} }$

Here, a = 22m, b = 120 m, c = 122 m

$\therefore \sf \: s \: = \dfrac{1}{2} (a + b + c)$

$\longrightarrow \sf \: s \: = \dfrac{1}{2} (22 + 120 + 122)$

$\longrightarrow \sf \: s \: = \dfrac{1}{2} \times 264$

$\longrightarrow\sf \: s \: =132$

$\sf \: \triangle \: = \sqrt{132(132- 22)(132 - 120)(132 - 122)}$

$\sf \: \triangle \: = \sqrt{132 \times 110 \times 12 \: \times 10}$

$\sf \: \triangle \: = 2 \times 3 \times 2 \times 2 \times 5 \times 11$

$\sf \: \triangle \: = 1320 {m}^{2}$

Now, We've to find the cost of levelling the ground at the rate of rupees 20 per m²

$\bigstar \: \boxed{ \sf \: Cost = \: Area \times Rate}$

$\longrightarrow \sf \: 1320 \times 20$

$\longrightarrow \sf \: Rs \: 26400$

$\therefore$ Area of the ground is 1320 m² and cost of levelling The ground at the rate of rupees 20 per m² is Rs 26400

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bcancel{\large{ \orange{\fbox{\tt{Âɴѕωєя࿐}}}}}$

$\sf{The \: area \:  and \: cost \: of \: leveling \: the \: ground \:  are }\\ \sf{ \: 1320 \: sq.m. \: and \: Rs.26400}$

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$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\blue{\overbrace{\blue{\underbrace{\color{lightgreen}{{ \blue\:{Explanation}}}}}}}$

We are given that The sides of the triangular ground are 22m,120m,122m

So, a = 22 m

b = 120 m

c = 122 m

$\bf{Area\:of \:triangle = A=\sqrt{s(s-a)(s-b)(s-c)}}$

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

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Substitute the values :

$\sf{s=\frac{22+120+122}{2}}$

$\sf{s=132}$

$\sf{A=\sqrt{132(132-22)(132-120)(132-122)}}$

$\sf{A=1320m^2}$

$\sf{Cost \: of \: leveling \: 1 \: sq.m. = Rs.20}$

$\sf{Cost \: of \: leveling \: 1320 \: sq.m. =} \\ \: \sf{ 1320 \times 20 = rs.26400}$

$\sf{The \: area \:  and \: cost \: of \: leveling \: the \: ground } \: \\ \sf{are \: 1320 \: sq.m. and \: Rs.26400}$

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