When 'a' is the side of a square then its diagonal is a*sqrt(2). Hence, if the diagonal of the square is 15*sqrt(6), then its side will be given by
Side = 15*sqrt(6)/sqrt(2) = 15*sqrt(2)*sqrt(3)/sqrt(2)
Area of square = side*side
= 15*sqrt(3)*15*sqrt(3) = 675 sq.cm.
675 squares of side 1 cm can be cut from the bigger square.
Each square of side 1 cm can be cut into two isosceles right triangles of side 1 cm.
Hence, the square can be divided into 675*2 = 1350 isosceles right triangles of side 1 cm.
A semi-circular park has a flowerbed of a certain width running along its arc on the inner side. The area of the park, including the flowerbed is 98*pi sq.m and the area of the park minus the flowerbed is 72*pi sq.m. Find the width of the flowerbed in meters.
Ann and Bill are 120cm and 165cm tall respectively. Their weights are 50kg and 64kg respectively. How much weight in kgs should Ann lose and Bill gain so that the height to weight ratio for both of them is the same?
Let the weight to be lost by Ann and that to be gained by Bill be x kgs. Their height to weight ratio will be 120/(50-x) = 165/(64+x) 120*(64+x) = 165*(50-x) 7680+120x = 8250 - 165x 570 = 285x x = 570/285 = 2