Question

A triangular park in a city has dimensions 30m,26m and 28m.
Find the area of the park and coast of planting grass in it at Rs.1.50 per m square​

Answer 1

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Correct Question:-

• A triangular park in a city has dimensions 30m × 26m × 28m. A gardener has to plant grass inside the park at Rs.150 per m² Find the amount to be paid to the gardener.

Solution:-

The dimension of the triangular park is 30m×26m×28m.

$⟹$S = $\dfrac{a+b+c}{2}$

$⟹$$\dfrac{30+26+28}{2}$

$⟹$ = 42m

The area of the triangular park is,

$\begin{gathered} :\implies \boxed{\pink{\bf Area = \sqrt{s(s - a)(s - b)(s - c)}}} \\ \\:\implies \sf \sqrt{42(42 - 30)(42 - 26)(42 - 28)} \\ \\:\implies \sf \sqrt{42 \times 12 \times 16 \times 14} \\ \\:\implies \sf \sqrt{6 \times 7 \times 6 \times 2 \times 4 \times 4 \times 7 \times 2} \\ \\:\implies \sf 6 \times 7 \times 2 \times 4 \\ \\ \large :\implies \underline {\boxed{\red{\sf 336 \: {m^{2}}}}\end{gathered}$

Therefore,

The amount paid to the gardener is,

• 336 × 1.50 = Rs 504

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Answer 2

Given :-

• Sides of the triangular park is 30 m , 26 m and 28 m

• Cost of planting grass is Rs 1.50 m²

To FinD :-

• Area of the park

• Cost of planting grass

SolutioN :-

Firstly we have to find Semi-perimeter of the park

$:\implies\boxed{ \red{ \bf s = \frac{a + b + c}{2}}} \\ \\:\implies \sf s = \frac{30 + 26 + 28}{2} \\ \\:\implies \sf s = \frac{84}{2} \\ \\:\implies \sf s = 42$

Now , Area of the park is

$:\implies \boxed{\blue{\bf Area = \sqrt{s(s - a)(s - b)(s - c)}}} \\ \\:\implies \sf \sqrt{42(42 - 30)(42 - 26)(42 - 28)} \\ \\:\implies \sf \sqrt{42 \times 12 \times 16 \times 14} \\ \\:\implies \sf \sqrt{6 \times 7 \times 6 \times 2 \times 4 \times 4 \times 7 \times 2} \\ \\:\implies \sf 6 \times 7 \times 2 \times 4 \\ \\ \large :\implies \underline {\boxed{\green{\sf 336 \: {m}^{2}}}}$

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Cost of planting grass in 1 m² = Rs 1.50

Cost of planting grass in 336 m² =

→ 1.50 × 336 = Rs 504