Question

The base of a triangular field is three times its height. if the cost of cultivating the field at rupees 46. 72 per metre square is rupees 2522.88, find its base and height.​

Answer 1

Total Cost of cultivating = ₹2522.88

Rate of cultivating = ₹46.72/m²

So, area = Cost/Rate

→ area = 2522.88/46.72

→ area = 54 m²

Now, given that base is three times of its height. So, if height is h, base is 3h

We know that area of triangle = 1/2 × base × height

→ 1/2 × 3h × h = 54

→ 3h²/2 = 54

Cross multiply,

3h² = 54 × 2

→ 3h² = 108

→ h² = 108/3

→ h² = 36

→ h = √36

→ h = 6 m

So, base = 3h = 3 × 6 = 18 m

Answer :- Base is 18 and height is 6 m.

Answer 2

Solution:-

Let the Height of the Triangular Field be "x" m.

=> Base of the Triangular Field = 3x m.

Now,

Area of Triangular Field = 1/2 × Base × Height

=> 1/2 × x × 3x

=> 3x^2 /2

Given that Cost of Cultivating the Field is 2522.88 Rupee.

Cost of 1m^2 = 46.72

=> Cost of 3x^2/2 m^2 = 46.72 × 3x^2/2

=> 2522.88 = 46.72 × 3x^2/2

$= > {x}^{2} = \frac{2522.88 \times 2}{3 \times46.72 } \\ \\ = > {x}^{2} = \frac{5045.76}{140.16} \\ \\ = > {x}^{2} = 36 \\ \\ = > x = 6$

Hence,

Height of Triangular Field = "x" = 6 m.

& Base of Triangular Field = 3x = 18m.