Area Problems The perimeter of a rectangle having area equal to 144 cm 2 and sides in the ratio 4 : 9 is 52 cm 60 cm 56 cm 64 cm 52 cm 60 cm 56 cm 64 cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP 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
Area Problems The base of right-angled triangle is 5 meters and hypotenuse is 13 meters . Its area will be? 28 m2 25m2 30m2 None of these 28 m2 25m2 30m2 None of these ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Altitude = ?(13)2 - (5)2= ?144 = 12m ? Area of the triangle = (5 x 12 ) / 2 m2= 30m2
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 50 cm 40 cm 30 cm 20 cm 50 cm 40 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.
Area Problems If the radius of a circle be reduced by 50%. Its area is reduced by? 65.5% 34.5% 39.5% 31.5% 65.5% 34.5% 39.5% 31.5% ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Original area = ? x (r/2)2 = ?r2/4Reduction in area = ? r2 - 3? r2/4? Reduction per cent = [ 3?r2/4 x 4/(?r2) x 100 ] %= 75%
Area Problems if the side of a square be increased by 4 cms. The area increased by 60 sq. cms . The side of the square is? 12 cm None of these 13 cm 14cm 12 cm None of these 13 cm 14cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let each side = x cmThen, (x + 4 )2 - x2 = 60? x 2 + 8x + 16 - x2 = 60? x = 5.5 cm
Area Problems The area of the largest circle that can be drawn inside a rectangle with sides 18cm by 14cm is 378 154 49 1078 378 154 49 1078 ANSWER EXPLANATION DOWNLOAD EXAMIANS APP The diameter is equal to the shortest side of the rectangle. So radius= 14/2 = 7cm. Therefore, area of circle = (r)2 = (22/7) x 49 = 154 cm2
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