Question

$\huge\mathtt\pink{QUESTION}$

Find the Area of the Triangular field of sides 55 m, 60 m, and 65 m. Find the cost of laying the grass in the triangular field at the rate of Rs 8 per m².
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Answer 1

$semi \: perimeter \: of \: the \: field \: is \: (s) = \\ \frac{50 + 65 + 55}{2} = \frac{180}{2} = 90 \\ \\ by \: herons \: formula = \\ \sqrt{s} (s - a)(s - b)(s - c) \\ \sqrt{90} (90 - 50)(90 - 65)(90 - 65) \\ \sqrt{90 (40)} (25)(25) \\ \sqrt{3600} \times 25 \times 25 \\ 60 \times 5 \times 5 \\ 300 \times 5 \\ = 1500 {m }^{2} \\ cost \: of \: lying \: grass = 1500 \times 8 = 12000$

Answer 2

❒ Concept Used :

• Heron's formula

❒ Side Of The Triangles :

• a = 55m
• b = 60m
• c = 65m

❒ By Heron's Formula :

$\sf{↠} \: \: {\underline{{\boxed{\sf{\red{ \: Area \: of \: triangle = \sqrt{s(s-a)(s-b)(s-c)} }}}}}}$

Where :

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

$\sf{{ ➻ \: s = \frac{55+60+65}{2} \: }{ \: }}$

$\sf{{ ➻ \: s = \red{90m}\: }{ \: }}$

ㅤㅤㅤㅤ ________________________

$\bf{{ ➯ \: Area \: of \: triangle =\: \sqrt{90(35)(30)(25)} = 1537.04{m}^{2} }{ \: }}$

❒ Now :

$\sf\pink{{Cost \: of \: laying \: grass = Area × 8 \: }{ \: }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⟼} \: \: \: \: \sf{{ ₹( 1537.04\times 8) \: }{ \: }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⟼} \: \: \: \: \sf{{₹12296.32 \: }{ \: }}$

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