Question

Find the cost of laying grass in a triangular field of sides 50m, 65m, and 65m at the rate of ₹ 7 per m^2

Answer 1

Answer:

The cost of laying grass is ₹10,500

Step-by-step explanation:

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Answer 2

GIVEN:

★Sides of the ∆ are 50m , 65m and 65m.

★Rate of laying grass is $Rs7m^{-2}$

TO FIND:

★Cost of laying the grass in the field.

CONCEPT USED:

★We would use the 'Heron's Formula' to find the area if the isosceles ∆ .

★Then the found area will be multiplied by its rate to find the cost.

ANSWER:

First side = 50m (a)

Second side = 65m (b)

Third side = 65m (c)

Now, By Herons Formula,

$\large\green{\boxed{A =\sqrt{s(s-a) (s-b) (s-c) }}}$

where s is the semi perimeter and A is area.

$\large\purple{\boxed{ s=\dfrac{a+b+c}{2}}}$

=>$s =\dfrac{50m+65m+65m}{2}$

=>$s =\dfrac{180m}{2}$

. °. $s = 90m$

______________________________________

Now, let area be denoted by A.

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

=>$A =\sqrt{90(90-50) (90-65) (90-65) m^{4}}$

=>$A =\sqrt{90×40×25×25m^{4}}$

=>$A =\sqrt{9×4×25×25×10×10m^{4}}$

=>$A =\sqrt{3×3×2×2×25×25×10×10m^{4}}$

=>$A = 3×2×25×10m^{2}$

. °.$A = 1500m^{2}$

Therefore area is 1500m^2.

______________________________________

Now, cost

$\large\red{\boxed{Cost = Area × Rate}}$

Let us denote cost by c.

=>$c =\dfrac{Rs1500×7m^{2}}{m^{2}}$

=>$c = Rs 10,500$

Therefore total cost is Rs 10,500.

$\huge\orange{\boxed{Cost=Rs10, 500}}$