Question

The sides of a triangular field are 60m, 56m and 52m. Find the cost of planting grass in the field at₹3.75 per square metre. If a space of 4m is to be left for gate to enter the field, find the cost of fencing it at ₹20 per metre.​

Answer 1

Answer:

given,

The sides of a triangular field is

a =60

b=56

c= 52

semi perimeter= a+b+c /2

= 60+56+52/2

=168/2

s =84

s-a =84-60=20

s-b=84-56=28

s-c=84-52=32

using Heron's formula

Area of triangle=√s(s-a)(s-b)(s-c)

=√84(84-24)(84-28)(84-32)

=√84×60×56×52

=√7×12×12×5×8×7×4×13

=√7×2×2×3×2×2×3×5×2×2×2×7×2×2×13

=√2×2×2×2×2×2×2×2×2×3×3×5×7×7×13

=√2×2×2×2×2×3×5×7×13

=√2×2×2×3×5×7×13

=√2×2×3×5×7×13

=√2×3×5×7×13

=2730m2

Total cost = area×rate

=2730×3.75

=10237.5 m2

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Answer 2

$\huge \tt \underline \orange {QUESTION}$

The sides of a triangular field are 60m, 56m and 52m. Find the cost of planting grass in the field at₹3.75 per square metre. If a space of 4m is to be left for gate to enter the field, find the cost of fencing it at ₹20 per metre.

$\huge \tt \underline \orange {Answer}$

Given:

• sides of triangle = 60,56 and 52 m
• cost of planting grass = ₹3.75/m²
• space left for gate = 4m
• cost for fencing = ₹20/m

To Find:

• total cost for planting grass
• total cost for fencing

Answer:

we know that sides of triangle are 60,56,52 m

now , as we don't know the height of the triangle

we will find the area through herons formulae

.°. Let the sides of the triangle be a,b,c such that

a = 60m b = 56m c = 52m

$\sf {\boxed {\<strong>pink { s\:=\:a+b+c/2 }}} [/tex</strong>]</p><h3>[tex] \implies$ S= 84m

now , we know that , herons formulae is equal to

$\sqrt{s(s - a)(s - b)(s - c)}$

$ar. \: of \: triangle \: = \: \sqrt{84(84 - 60)(84 - 56)(84 - 52)}$

$= \sqrt{84 \times 24 \times 28 \times 32}$$\sqrt{2 \times 2 \times 3 \times 7 \times 2 \times 2 \times 2 \times 3 \times 2 \times 2 \times 7 \times 2 \times 2 \times 2 \times 2 \times 2}$

$= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 7$

$ar. \: of \: triangle = 1344 \: {m}^{2}$

Now , cost of planting 1 m² grass= ₹3.75

cost , of planting 1344 m² of grass = 3.75 ×1344

$\implies$ hence , cost of planting grass in the park = ₹5040

Now , perimeter of triangle = S*2 = 84×2perimeter = 168m

total perimeter which is to be fences = 168 - 4 m( °.° 4m is to be left for gate )

therefore , total perimeter which is to be fences = 164 m

cost of fencing 1m = ₹20therefore ,cost of fencing 164 m = 164 × 20

hence , cost of fencing is equal to ₹3280