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.

Answer 1

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.