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Question
The sides of the triangular ground are 22 m, 120 m and 122 m. Find the area and cost of levelling the ground at the rate of ₹ 20 per m2
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Solution
The sides of the triangular ground are 22 m, 120 m and 122 m
a = 22 m, b = 120 m, c = 122 m
s = `("a" + "b" + "c")/2`
`(22 + 120 + 122)/2 "m"`
= 132
s – a = 132 – 22 = 110 m
s – b = 132 – 120 = 12 m
s – c = 132 – 122 = 10 m
= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`
= `sqrt(132 xx 110 xx 12 xx 10)`
= `sqrt(2^2 xx 3 xx 11 xx 11 xx 10 xx 2^2 xx 3 xx 10)`
= `sqrt(2^4 xx 3^2 xx 10^2 xx 11^2)`
= 4 × 3 × 10 × 11
= 1320 sq.m
Cost of levelling for one sq.m = ₹ 20
Cost of levelling the ground = ₹ 1320 × 20
= ₹ 26400
Area of the ground = ₹ 1320 sq.m
Cost of levelling the ground = ₹ 26400
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