the sum of the circumference of a circle and the perimeter of the rectangle is 480cm. the area of the rectangle is 168cm². if the ratio of the radius of the circle to the breadth of the rectangle is 19:2, find the radius of the circle and the length of the rectangle.
Answers
Step-by-step explanation:
let the radius of circle be 19x and breadth of rect be 2x.
perimeter of rect=2 (l+b),circumference of circle =2×22/7×19x
168=2 (l+2x)+44/7×19x
84=l+2x+22/7×19x
Now solve for x
Answer:
Area of the rectangle = 168 cm2
Ratio of radius of the circle and breadth of the rectangle = 19 : 2
Let the radius of the circle be 19x and breadth of the rectangle be 2x.
WKT, Area of rectangle = l*b
l*b = 168
l*2x = 168
l = 84/x cm
WKT, circumference of a circle = 2π r
Perimeter of rectangle = 2(l + b)
Sum of circumference of a circle and perimeter of a rectangle = 480 cm
2π r + 2(l + b) = 480
2*(22/7)*19x + 2[(84/x) + 2x] = 480
36x2 - 140x + 49 = 0
x = 7/2
So, breadth of rectangle = 2(7/2) = 7 cm
length of rectangle = 84/(7/2) = 24 cm
Diagonal of rectangle = √[242 + 72]
= √[576 + 49]
= √625
= 25 cm
Let the radius of new circle be 'R'.
Radius of new circle is 28% of the diagonal of rectangle = (28/100)*25
= 7 cm.
Area of new circle = π R2
= (22/7)*(7)2
= 154 cm2.