Question

Find the cost of leveling the ground in the from of a triangle having Its side as 70 cm, 50
cm, and 60 cm, at 7 per square meter.​

Answer 1

Given :-  

• The ground in the form of a triangle have sides as 70 cm, 50cm, and 60 cm

• It can be levelled at Rs. 7 per square meter.

To Find :-  

• The cost of levelling that ground.  

Solution :-  

~Here, we’re given the sides of a triangle and we need to find the cost of levelling it at Rs. 7 per m². Firstly, we need to find the area of the triangle by Heron’s formula and then multiply it by the given cost.  

As we know that ,  

$\sf \bigstar \;\; Area\;of\;a\;triangle = \sqrt{s(s-a)(s-b)(s-c)}$ 

Where,  

• s is the semi-perimeter  
• a,b,c are the sides of triangle  

Finding the semi-perimeter :-  

$\sf \implies s = \dfrac{70+60+50}{2}$ 

$\sf \implies s = \dfrac{180}{2}$ 

$\sf \implies s = 90\;cm$

Finding the area :-  

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

$\sf \implies \sqrt{90(90-70)(90-60)(90-50)}$

$\sf \implies \sqrt{90(20)(30)(40)}$

$\sf \implies \sqrt{2160000 }$

$\sf \implies 600\sqrt{6\;cm }$

~ As, the cost given to us is in meter so we will convert our area in meter.  

$\sf \bullet \;\; 1\;cm^{2} = \dfrac{1}{10000} \;m^{2}$

$\sf \implies 600 \sqrt{6\;cm} = \dfrac{600 \sqrt{6}}{10000}$ 

Finding the cost of levelling :-  

$\sf \bullet \;\; 1\;m^{2} = Rs.\; 7$ 

$\sf \implies \dfrac{600 \sqrt{6}}{10000} = \dfrac{600 \sqrt{6}}{10000} \times 7$ 

$\sf \implies Rs.\;1.02$ 

Therefore,  

• The cost of levelling of the ground is Rs 1.02  

Answer 2

ANSWER

$\red\bigstar$ Cost of leveling the ground = ₹ 1.02

SOLUTION

Let us assume that the sides of the triangles are a, b and c.

Here,

a = 70cm.

b = 50 cm.

c = 60 cm.

$\boxed{\sf Cost \: of\: leveling\: the\: ground = Area \:of \:the\: ground * Rate \:of \:leveling}$

$\boxed{\sf Area\; of \: triangle = \sqrt{s(s-a)(s-b)(s-c) } }$

Where , s is the semi-perimeter of the triangle.

$\sf s = \dfrac{a+b+c}{2}$

$\implies \dfrac{\sf 70+50+60}{2}$

$\implies \dfrac{\sf 180}{2}$

$\implies$ Semi - perimeter (s) = 90.

Area

$\sf Area\; of \: triangle = \sqrt{s(s-a)(s-b)(s-c) }$

$\implies \sf Area\; of \: triangle = \sqrt{90(90-70)(90-50)(90-60) }$

$\implies \sf Area\; of \: triangle = \sqrt{90*20*40*30 }$

$\implies \sf Area\; of \: triangle = \sqrt{2160000 }$

$\implies \sf Area\; of \: triangle = 600\sqrt{6} cm^2.$

Now,let us substitute √6 = 2.45.

$\implies$ Area of triangle = 600 × 2.45

$\implies$ Area of triangle = 1470 cm².

$\implies \sf Area \; of \; triangle = \dfrac{1470}{10000}$

$\implies$ Area of triangle = 0.147 m².

Cost of Leveling

$\sf Cost \: of\: leveling\: the\: ground = Area \:of \:the\: ground * Rate \:of \:leveling$

Here,

Area of the ground = 0.147 m².

Rate of leveling = ₹7/m².

$\implies \sf Cost \: of\: leveling\: the\: ground = 0.147 * 7$

$\implies$ Cost of leveling the ground = ₹ 1.029 ≈  ₹ 1.02