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 

Answer 1

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