Question

the ratio of base to hight of a triangular field is 3:1 if cost of cultivating the field at Rs. 28 per sq.m is Rs 9450 find it base and hight​

Answer 1

the height of triangle is 15m and base is 45m.

Answer 2

The base and the height of the triangular field is 45 m and 15 m respectively.

Explanation:

Given : The ratio of base to height of a triangular field is 3:1.

Let 3x be the base and x be the height of the triangular field.  (1)

Area of triangle = $\dfrac{1}{2}\times base\times height$

Then Area of triangular field = $\dfrac{1}{2}\times (3x)\times(x)$

$\dfrac{3}{2}x^2$

Cost of cultivating the field at Rs. 28 per sq.m = 28 x Area of triangular field

$=28\times\dfrac{3}{2}x^2$

$=42x^2$

Since Cost of cultivating the field  is Rs 9450 (given).

Then, $42x^2=9450$

$x^2=\dfrac{9450}{42}=225$

$\Rightarrow\ x=\sqrt{225}=\pm15$

Since side cannot be negative , so x= 15

From (1) , base = 3 (15)= 45 m

height = 15 m

Hence, the base and the height of the triangular field is 45 m and 15 m respectively.

# Learn more :

If hight and base of a triangle are in the ratio 4:3.If its area is 394cm^2.Then find hight and base.

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