Question

The length of three sides of a triangular field of village of Paholampur are 26meter, 28meter
and 30meter.
(i) Let us write by calculating what will be the cost of planting grass in the triangular field
at therate of₹5 per sq. meter.
(ii) Let us write by calculating how much cost will be for fencing around three sides at the
rate of 18 per meter leaving a space 5 meter for constructing entrance gate of that
triangular field.​

Answer 1

Answer:

1) 1680 Rupees

2) 1422 Rupees

Step-by-step explanation:

This question will require the application of 'Heron's Formula'.

Heron's Formula :-   Area Of Triangle=$\sqrt{s(s-a)(s-b)(s-c)$

where S is the semi-perimeter of the triangle.

S= (a+b+c)/2 ;  a,b and c are the sides of the triangle.

1) Calculating 'S' for the given triangular field,

  S=(26+28+30)/2

    =42 m

 Now to find the area, apply 'Heron's Formula'.

 Δ=$\sqrt{42(42-26)(42-28)(42-30)}$

 which gives

  $\sqrt{42(16)(14)(12)} \\= \sqrt{(7*6)(4*4)(7*2)(2*6)$

 = (7*6*4*2)

 = 336 square metres

The rate of planting the grass is 5 rupees per square metre.

Applying unitary method,

we find that 1680 rupees, will be needed to grass the field completely.

2) Find the perimeter of the field, which comes out to be 84 metres.

    Removing 5 metres for gate gives 79 metres.

   Fencing costs 18 rupees per metre.

   Apply unitary method,

   cost for fencing 79 metres will be 1422 rupees.

This will be the answer.

Answer 2

$\large\bf\underline{Given:-}$

• length of three sides of a triangular are 26m, 28m and 30m

$\large\bf\underline {To \: find:-}$

• cost of planting grass in the triangular field at therate of₹5 per sq. meter
• cost fencing around three sides at the rate of 18 per meter leaving a space 5 meter for constructing entrance gate of that triangular field.

$\huge\bf\underline{Solution:-}$

• length of three sides of a triangular field :- 26m, 28m and 30m

(i) cost of planting grass in the triangular field at therate of₹5 per sq. meter.

$\tt \large \: s = \frac{a + b + c}{2}$

Let

• a = 26
• b = 28
• c = 30

$\tt \longrightarrow \: s = \frac{26 + 28 + 30}{2} \\ \\ \tt \longrightarrow \:s = \cancel\dfrac{84}{2} \\ \\ \tt \longrightarrow \:s = 42$

✝ By Heron's Formula:-

$\tt \: area \: of \triangle = \sqrt{s(s - a)(s - b)(s - c)}$

finding area of triangular field :-

$: \mapsto \tt \: \sqrt{42(42 - 26)(42 - 28)(42 - 30)} \\ \\ : \mapsto \tt \: \sqrt{42 \times 16 \times 14 \times 12} \\ \\ : \mapsto \tt \: \sqrt{112896} \\ \\ : \mapsto \tt \: 336 {m}^{2}$

Now , finding cost of planting grass in the triangular field at therate of₹5 per sq. meter

»» 336 × 5

»» Rs 1680

Hence ,

cost of planting grass = Rs 1680

$\rule{200}3$

(ii) finding cost fencing around three sides at the rate of 18 per meter leaving a space 5 meter for constructing entrance gate of that triangular field.

Perimeter of triangle = 28 + 26 + 30

Perimeter of triangle = 84m

leaving space 5m for entrance gate = 84 - 5

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 79m

So fencing can be done around the field of 79m

Now,

• Rate = 18 per meter

cost of fencing around the field = 79 × 18

cost of fencing around the field =Rs1422

Hence

✝ Cost of fencing the field = Rs 1422.

$\rule{200}3$