Question

the area of a circular field is equal to the area of a rectangular field. the ratio of the length and the breath of the rectangular field is 24:11 respectively and perimeter is 100 meters. what is the diameter of the circular field

Answer 1

Answer:

10 meter

Step-by-step explanation:

given that,

in a rectangular feild

ratio of length and breadth

= 24:11

let the common ratio be x

then,

sides will be

24x and 11x

also given

perimeter of rectengle

= 100 m

so,

ATQ,

given,

2(l + b) = 100

putting the length and breadth

2(24x + 11x) = 100

2(35x) = 100

70x = 100

x = 100/70

x = 10/7

now,

length = 24x

= 24(10/7)

= 240/7

breadth = 11x

= 11(10/7)

= 110/7

now,

given that,

area of circular feild = area of rectangular feild,

so,

πr² = lb

22/7 × r² = 110/7 × 240/7

r² = 110/7 × 240/7 × 7/22

r² = 5 × 240/7

r² = 1200/7

r = √1200/7

r = 4.94

r = 5 meter (approx)

so,

radius of rectangular feild = 5 meter

now,

diameter = 2 × radius

= 2 × 5

= 10 meter

so,

diameter of the circular feild = 10 meter