Question

The base of a triangular field is three times its height. If the cost of cultiva g the field
at 35 per hectare is 486, find its base and height (1 hectare = 10000 m^2)​

Answer 1

$\bigstar \underline{\underline{\sf Given:-}}$

• Base of a triangular field = 3×height
• Cost of cultivating field at 35 per hectare= 486
• 1 hectare = 10000 m².

$\bigstar \underline{\underline{\sf To\ find:-}}$

• Base & height.

$\bigstar \underline{\underline{\sf Solution:-}}$

Let the height be 'h'

Then, base = 3h

We know:

$\leadsto \underline{\boxed{\sf Area\ of\ triangle = \frac{1}{2}bh}}$

Where,

b = base

h = height

$\mapsto \sf Area=\frac{1}{2} bh\\\\:\implies \sf Area= \frac{1}{2} (3h)(h)\\\\:\implies \sf Area = \frac{3h^2}{2}$

Given that,

The rate of cultivating the field = Rs. 35

Total cost = Rs. 486.

Total cost = area of the triangular field × Rs. 35

$:\implies \sf 486 = \frac{3h^2}{2} \times \frac{35}{10000} \\\\:\implies \sf \frac{486}{35} \times \frac{2}{3}\times 1000 = h^2 \\\\:\implies \sf h^2 = 92571.42\\\\:\implies \boxed{\sf h = 304.25}$

We have base = 3h

So,

Base = 3(304.25)

         = 912.6

Hence,

Base = 912.6m.

Height = 304.25m.

_______________

Answer 2

$\bigstar \underline{\underline{\sf Given:-}}$

Base of a triangular field = 3×height

Cost of cultivating field at 35 per hectare= 486

1 hectare = 10000 m².

$\bigstar \underline{\underline{\sf To\ find:-}}$

Base & height.

$\bigstar \underline{\underline{\sf Solution:-}}$

Let the height be 'h'

Then, base = 3h

We know:

$\leadsto \underline{\boxed{\sf Area\ of\ triangle = \frac{1}{2}bh}}$

Where,

b = base

h = height

$\mapsto \sf Area=\frac{1}{2} bh\\\\:\implies \sf Area= \frac{1}{2} (3h)(h)\\\\:\implies \sf Area = \frac{3h^2}{2}$

Given that,

The rate of cultivating the field = Rs. 35

Total cost = Rs. 486.

Total cost = area of the triangular field × Rs. 35

$:\implies \sf 486 = \frac{3h^2}{2} \times \frac{35}{10000} \\\\:\implies \sf \frac{486}{35} \times \frac{2}{3}\times 1000 = h^2 \\\\:\implies \sf h^2 = 92571.42\\\\:\implies \boxed{\sf h = 304.25}$

We have base = 3h

So,

Base = 3(304.25)

         = 912.6

Hence,

Base = 912.6m.

Height = 304.25m.

_______________