Question

the side of triangle is 55m,300m and 300m.its area is equal to (7/15) the area of circular park.what is the perimeter of the circular park​

Answer 1

Answer:

The Perimeter of the circular park is approximately 219.42m

Step-by-step explanation:

We are given,

Sides of the Triangle is 55m, 300m, 300m

Area of Tiangle = (7/15) × Area of a circular park.

Now, we must find the area of the triangle,

So, we must use the Heron's Formula,

Area = √(s(s - a)(s - b)(s - c))

Here,

a, b, and c are the sides and s is the semi-perimeter(Half of perimeter)

a = 55m

b = 300m

c = 300m

s = (300 + 300 + 55)/2

s = 327.5

Thus,

Area = √(327.5(327.5 - 55)(327.5 - 300)(327.5 - 300))

Area = √(327.5 × 272.5 × 27.5 × 27.5)

Area = 27.5√(327.5 × 272.5)

Area = 27.5√(89,243.75)

Area = 27.5 × 298.73

Area = 8,215.075 m²

Now,

The Area of Circular park = (7/15) × Area of Triangle

Area = (7/15) × 8,215.075

Area = 57,505.525/15

Area = 3,833.70

We know that,

Area of Circle = πr²

πr² = 3833.70

3.14 × r² = 3833.70

r² = 3833.70/3.14

r² = 1220.92

r = √1220.92

r = 34.94

Perimeter of a circle is nothing but its Circumference

C = 2πr

C = 2 × 3.14 × 34.94

C = 219.42 m

Thus,

The Perimeter of the circular park is approximately 219.42 m

Hope it helped and believing you understood it........All the best