A geometry problem by sara sharma

Geometry Level 2

The base of a triangular field is 3 times it's altitude. If the cost of watering the field at Rs. 96 per hectare is Rs. 3600 then find the measure of base and hight. ( In metres)

800,2400 400, 1200 900, 300 500, 1500

Sara Sharma by sara sharma , 18, India

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1 solution

1 h e c t a r e = 10000 m 2 1~hectare=10000~m^2

So the area of the triangular field is

R s . 3600 ( 10000 m 2 R s . 96 ) = 375000 m 2 Rs.~3600\left(\dfrac{10000~m^2}{Rs.~96}\right)=375000~m^2

We know that area of a triangle is 1 2 a b \dfrac{1}{2}ab where a a is the altitude and b b is the base, so we have

375000 = 1 2 ( a ) ( 3 a ) 375000=\dfrac{1}{2}(a)(3a)

a = 500 a=500

It follows that b = 3 ( 500 ) = 1500 b=3(500)=1500

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