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Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs $7\; per\; m^{2}$

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$Rs.10500$

To find the cost, first we have to find the area of this triangular field.

$Let \; sides\; be\; a = 50\; cm ; b = 65\; cm ; c = 65 \; m$

$Semi\; perimeter(s) = \frac{a+b+c}{2}$

$= \frac{50+65+65}{2}$

$= \frac{180}{2}$

= 90

Area of Triangular field:

$By\; herons\; formula =\sqrt{S\left ( S-a \right )\left ( S-b \right )\left ( S-c \right )}$

$=\sqrt{90\left ( 90-50\right )\left ( 90-65 \right )\left ( 90-65 \right )}$

$=\sqrt{90\times 40\times 25\times 25}$

$=\sqrt{9\times 10\times 4\times 10\times \left ( 5^{} \right )^{2}\times \left ( 5 \right )^{2}}$

= $3\times 10\times 2\times 5^{2}$

= $30\times 2\times 25$

$= 1500m^{2}$

$Rate\; of\; laying \; grass = 7\; Rs \; per\; m^{2}$

$Cost\; of \; laying \; grass\; for\; 1500 m^{2} = Rs (7 \times 1500)$

$= 10500\; Rs$

$Hence\; the \; answer\; is\; 10500 Rs.$

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infoexpert21

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