Question

The base of a triangular field is three times its height. If the cost of sowing the field at ₹64 per square metre is ₹ 864, then its base =​

Answer 1

Required Answer :

The base of the trianglular field = 9 m

Given :

• The base of a triangular field is three times its height.
• Rate of sowing the field = Rs. 64
• Total cost of sowing the field = Rs. 864

To find :

• Base of the trianglular field

Solution :

To calculate the base of the field, firstly we will calculate the area of the trianglular field. To find the area of the field, divide the total cost of sowing the field by the rate of sowing the field.

[While finding the total cost of sowing we multiply the area by the rate of sowing. So, to find the area divide the total cost by the rate.]

⇒ Total cost of sowing = Area × Rate of sowing

So,

⇒ Area = Total cost of sowing ÷ Rate of sowing

⇒ Area = 864/64

⇒ Area = 432/32

⇒ Area = 216/16

⇒ Area = 108/8

⇒ Area = 13.5

Therefore, the area of the trianglular field = 13.5 m²

Let us assume that :

⇒ Height of the trianglular field = x metre

⇒ Base of the trianglular field = 3(Height)

⇒ Base of the trianglular field = 3x metre

Using formula,

• Area of triangle = ½ × b × h

where,

• b denotes the base
• h denotes the height

Substituting the given values :

⇒ 13.5 = ½ × 3x × x

⇒ 13.5 × 2 = 3x²

⇒ 27 = 3x²

⇒ 27/3 = x²

⇒ 9 = x²

⇒ Taking square root on both the sides :

⇒ √9 = x

⇒ √(3 × 3) = x

⇒ ± 3 = x

As we know that the side of triangle cannot be negative. So, the negative sign will get rejected.

⇒ ± 3 Reject -ve = x

⇒ 3 = x

The value of x = 3

Substituting the value of 'x' in the base of trianglular field :

⇒ Base = 3x

⇒ Base = 3(3)

⇒ Base = 9

Therefore, the base of the trianglular field = 9 m