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83. Length of a rectangle is 12 cm more than itsbreadth and it has a perimeter of 200 cm. What willbe diameter of a circle whose area matches thearea of this rectangle?

Answer»

perimeter=2( l+b); 200=2(l+b); 200=2(12+2b); 200=24 + 4b; 200-24=4b; 176=4b; b=176/4=44

let breath = x cmlength = x+122(length+ breath)=perimeter2(x+12+x)=2002x+12= 1002x= 100-12=88x= 88/2= 44.so breath = 44.cmlength = 44+12=56cmarea of rectangle= length×breath= 44×56= area of circle let radius of circle =rπr^2= 44×5622/7×r^2= 44×56r^2= 44×56×7/22 = 2×56×7r= √2×56×7 =√2×2×2×2×7×7 = 2×2×7= 28cmdiameter = 2r= 2×28=56cm


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