Question

the ratio of base to height of a triangular field is 3 : 1. If the cost of cultivating the field at Rs.28 per sq. m is Rs.9450, find its base and height.​

Answer 1

Answer:

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

2

1

×base×height

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

2

1

×(3x)×(x)

\dfrac{3}{2}x^2

2

3

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=28×

2

3

x

2

=42x^2=42x

2

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

Then, 42x^2=945042x

2

=9450

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

2

=

42

9450

=225

\Rightarrow\ x=\sqrt{225}=\pm15⇒ x=

225

=±15

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.