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प्रश्न
The cost of fencing a triangular field at the rate of Rs.15 per m is Rs.900. If the lengths of the triangle are in the ratio 3:4:5, find the area of the triangle and the cost of cultivating it at Rs.48 per kg sq.m.
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उत्तर
Let the Perimeter of the triangular plot of land = P
∴ P x 15 = 900
⇒ P = `(900)/(15)`
= 60
Let the sides of the triangular plot of land = 3x, 4x and 5x
So,
3x + 4x + 5x
=60
⇒ x = 5
So, the sides of the triangular plot of land
= 3 x 5, 4x 5 and 5 x 5
= 15m, 20m, 25m
We know that, Area of a Triangle whose sides are a, B, and c and semiperimeter is s given by `sqrt("s"("s" - "a")("s" - "b")("s" - "c")) ; "s" = ("a" + "b" + "c")/(2)`
For a triangle whose sides are cm, cm and cm
ie a= 15 b = 20 and c = 25, s = `(60)/(2)` = 30
Area
= `sqrt(30(30 - 15)(30 - 15)(30 - 20)(30 - 25)`
= `sqrt(30(15)(10)(5)`
= `sqrt(22500)`
= 150cm2
Cost of cultivating 1m2 = Rs.48
Cost of cultivating 150m2
= Rs.48 x 150
= Rs.7200.
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