Area Problems
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Area of square = (Side)2 = 202= 400 sq cm ? Area of rectangle = 1.8 x 400 = 720 sq cm Let length and breadth of rectangle be 5k and k respectively.Then, according to the question, 5k x k = 720? 5k2 = 720 ? k2 = 720/5 = 144? k = ?144 = 12 cm Perimeter of rectangle = 2(5k + k) = 12k= 12 x12 = 144 cm
Let l = 4k and b = 9kArea of rectangle = l x b144 = 4k x 9k ? k2 = 144/36 ? k2 = 4? k = 2? l = 8 cm and b = 18 cmPerimeter of rectangle = 2(l + b)= 2(8 + 18)= 2 x 26= 52 cm
Original circumference = 2?r New circumference = (150 /100) x 2 ?r = 3?r 2?R = 3?r? R = 3r/2 Original area = ?r2New area = ?R2= ?9r2 / 4 = 9?r2/4Increase in area = (9?r2/4 ) - (?r2)= (5/4) ?r2Req. increase per cent = [{(5/4) ?r2} / {?r2}] x 100 = 125 %
EXAMIANS