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Question
The base of a triangle field and its height are in the ratio 2:5. If the cost of cultivating the field at Rs.42 per sq. m is Rs.7560, find its base and height.
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Solution
Let the Area of the triangular plot of land = A m2
∴ A x 42 = 7560
⇒ A = `(7560)/(42)`
= 180
Let the base and height of the plot be 2x and 5x respectively
We know that, Area of a triangle
= `(1)/(2)"b.h" "i.e"(1)/(2)("Base" xx "Height")`
⇒ 180 = `(1)/(2)(2x).(5x)`
⇒ 5x2 = 180
⇒ x2 = `(180)/(5)`
= 36
⇒ x = 6
⇒ Base = 2(6) = 12m; Height = 5(6) = 30m.
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