Question

a field is in the form of a right triangle with sides 90m and 120m respectively conataining the right angle. calculate the cost of levelling the field at the rate of rupees 20 per sq m.

Answer 1

DIAGRAM :

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Given : A field is in the form of a right angled triangle with sides 90cm and 120m respectively containing the right angle.

To Find : Cost of levelling the field @ ₹20 per m².

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Here, two sides of right angled triangle is given as 90cm and 120cm.

We'll find the area of the the field which is in the right angled triangle form.

$\: \:$

For finding the area of a right angled triangle, formula is given as :

$\: \:$

$\star\underline{\boxed{\sf\pink{Area_{(right ∆)} = \frac{1}{2} \times product \: of \: two \: sides}}}$

$\: \:$

$\sf:\implies \: Area_{(right ∆)} = \dfrac{1}{2} \times 90 \times 120 \\ \\ \\ \sf:\implies \: Area_{(right ∆)} = \frac{90 \times \cancel{120}}{ \cancel{2}} \\ \\ \\ \sf:\implies \: Area_{(right ∆)} = 90 \times 60 \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{Area_{(right ∆)} = 5400 \:cm {}^{2} }}} \: \bigstar$

$\:$

$\sf\therefore{\underline{Hence, \: the \: area \: of \: the \: field \: is \: \bold{5400 \: {cm}^{2} }.}}$

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Now we'll find the cost of levelling the field.

$\:$

$\sf:\implies \: cost \: of \: levelling \: 1 {m}^{2} = 20 \\ \\ \\ \sf:\implies \: cost \: of \: levelling \: 5400 {m}^{2} = 5400 \times 20 = \bold{₹108000}$

$\: \:$

$\sf\therefore{\underline{Hence, \: the \: cost \: of \: levelling \: the \: field \: at \: the \:rate \: of \: rupees \: 20 \: per \: sq.m \: is \: \bold{₹108000} }}$

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Answer 2

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