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  • The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m^{2} is Rs 918.

Write True or False and justify your answer:

The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3\; per\; m^{2} is Rs 918.

Answers (1)

[True]

Let\; a = 51 \; m, b = 37\; m \; and \; c = 20\; m

                          

S=\frac{51+37+20}{2}=\frac{108}{2}=54m

We know that using Heron’s formula

Area\; of \; triangle AB=\sqrt{S\left ( S-a \right )\left ( S-b \right )\left ( S-c \right )}

=\sqrt{54\left ( 54-51 \right )\left ( 54-37 \right )\left ( 54-20 \right )}

=\sqrt{54\times 3\times 17\times 34}

=\sqrt{9\times 3\times 2\times 3\times 17\times 17\times 2}

=\sqrt{3\times3\times 3\times 3\times 2\times 2\times 17\times 17}

=3\times 3\times 2\times 17

= 306m^{2}

To find cost :

 Cost of levelling 1 m2 = Rs 3

\therefore Cost\; of\; levelling\; 306\; m^{2} = \; 3 \times 306 = Rs.\; 918

Therefore the given statement is true.

Posted by

infoexpert21

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