Area Problems If the base of a rectangular is increased by 10% and the area is unchanged , then the corresponding altitude must to be decreased by? 91/11 % 111/9 % 10% 11% 91/11 % 111/9 % 10% 11% ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let base = b and altitude = h Then, Area = b x h But New base = 110b / 100 = 11b / 10Let New altitude = HThen, Decrese = (h - 10h /11 )= h / 11? Required decrease per cent = (h/11) x (1 / h ) x 100 %= 91/11 %
Area Problems A circle and a square have same area. The ratio of the side of the square and the radius of the circle is? ?? : 1 1 : ?? ? : 1 1 : ? ?? : 1 1 : ?? ? : 1 1 : ? ANSWER EXPLANATION DOWNLOAD EXAMIANS APP ? Area of square = Area of circle ? x2 = ?r2? x/r = ?? = ? ? : 1
Area Problems The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be: 9 cm 41 cm 20 cm 18 cm 9 cm 41 cm 20 cm 18 cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP √l2 + b2 = √41. Also, lb = 20. (l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81 ⟹ (l + b) = 9. ∴ Perimeter = 2(l + b) = 18 cm
Area Problems The difference between the circumference and the radius of a circle is 37 cm. The area of a circle is? 259 sq. cm 148 sq. cm 154 sq. cm 111 sq. cm 259 sq. cm 148 sq. cm 154 sq. cm 111 sq. cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP ? 2?r - r = 37? [(2 x 22/7) -1]r= 37? 37r / 7= 37? r = 7 So, area of the circle =(22/7) x 7 x 7 cm2= 154 cm2
Area Problems If the ratio of the area of two square is 9 : 1 the ratio of their perimeters is? 9:1 3:1 1:3 3:4 9:1 3:1 1:3 3:4 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let the area of square be (9x)2 m2 and (x2) m2Then, their sides are (3x) m and x metres respectively? Ratio of their perimeters = 12x / 4x=3:1
Area Problems The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and the breadth is increased by 5 cm, the area of the rectangle is increased by 75 cm 2 . Therefore , the length of the rectangle is? 20 cm 40 cm 50 cm 30 cm 20 cm 40 cm 50 cm 30 cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let breadth = b, length = 2b? Area of rectangle = 2b x b = 2b2As per question. ? (2b - 5 ) (b + 5 ) = 2b2 + 75? 5b = 75 + 25? 5b = 100? b = 100 / 5 = 20Hence, length of the rectangle =2b = 2 x 20 = 40 cm.
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