Question

The sides of a triangular ground are 40m,70m and 90m. Find the cost of levelling the ground at the rate of ₹7.50 per sq. m. Take √5=2.24​

Answer 1

Step-by-step explanation:

Given :-

The sides of a triangular ground are 40m,70m and 90m.

To find :-

Find the cost of levelling the ground at the rate of ₹7.50 per sq. m. Take √5=2.24

Solution :-

The sides of a triangular ground are 40m,70m and 90m.

Let a = 40 m

Let b = 70 m

Let c = 90 m

We know that

Area of a triangle whose sides are a,b and c units by Heron's formula

= √[S(S-a)(S-b)(S-c)] sq.units

Where, S = (a+b+c)/2 units

On substituting these values in the above formula

S = (40+70+90)/2

=> S = 200/2 m

=> S = 100 m

Now,

Area of the triangular ground

=> √[100(100-40)(100-70)(100-90)] sq.m

=> √[(100)(60)(30)(10)]

=> √1800000

=> √(180×10000)

=> √(2×2×9×5×100×100)

=> 2×2×3×100×√5

=> 1200√5 sq.m

Given that

√5 = 2.24

Now, Area = 1200×2.4 sq.m

=> Area = 2880 sq.m

Area of the triangular ground = 2880 sq.m

The cost of levelling the ground at the rate of

₹ 7.50 per sq. m.

Total cost of levelling the total ground of 2880 sq.m = ₹ 7.50 × 2880

= ₹ 21600

Answer:-

The total cost of levelling the ground is

₹ 21600

Used formulae:-

→ Area of a triangle whose sides are a,b and c units by Heron's formula =

√[S(S-a)(S-b)(S-c)] sq.units

• Where, S = (a+b+c)/2 units