Question

Find the cost of laying grass in a triangular field of sides 50 m, 65 m, and 65 m at the rate of Rs 7 per m2.

Answer 1

Semi perimeter=(a+b+c)/2
=180/2=90  m.
Area:\sqrt{s(s-a)(s-b)(s-c)}s(s−a)(s−b)(s−c)​ 
⇒\sqrt{90(90-65)(90-65)(90-50)}90(90−65)(90−65)(90−50)​ 
⇒\sqrt{90*25*25*40}90∗25∗25∗40​ 
=\sqrt{5 ^{6}*2 ^{4} *3^{2} }56∗24∗32​ 
⇒125*4* 3125∗4∗3 
⇒1500 m21500m2 
Cost:1500*7
=Rs.10500
Ans:Rs.10500.
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Answer 2

⇝Given :

Dimensions of triangular field = 50m,65m,65m

Rate = Rs 7 m²

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⇝To Find :

Total cost of laying grass = ?

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⇝Formula Used :

${\red{\bigstar{\orange{\underbrace{\underline{\mathfrak{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}}}}}$

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⇝Solution :

❒First finding Area :

${\mapsto{\bf{S = \frac{a + b + c}{2} }}}$

${\leadsto{\sf{ \frac{50 + 65 + 65}{2} }}}$

${\leadsto{\sf{ {\cancel\frac{180}{2} }}}}$

${\red{\underline{\bf{Semi - Perimeter = 90m}}}}$

${\mapsto{\bf{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}$

${\leadsto{\sf{ \sqrt{90(90 - 50)(90 - 65)(90 - 65)} }}}$

${\leadsto{\sf{ \sqrt{90 \times 40 \times 25 \times 25} }}}</p><p>[tex]{\leadsto{\sf{ \sqrt{90 \times 40 \times 25 \times 25} }}}$

${\red{\underline{\bf{1500 m²}}}}$

❒Now :

${\leadsto{\text{Cost of laying grass in 1m² = Rs 7}}}$

${\leadsto{\sf{Cost \: of \: laying \: gras s \: in \: 1500m² = 1500 \times 7}}}$

${\purple{\large{:{\longmapsto{\underline{\boxed{\bf{Rs 10,500}}}}}}}}$

❒So,

Cost of laying grass in this triangular field is Rs 10,500 .

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