Bissoy.com
Doctors Medicines MCQs Q&A

The sum of the area of two rectangles is 384 cm2 and the breadth of both rectangles is equal to the diameter of the circle whose area is 16π cm2. If the difference between the lengths of both rectangles is 24 cm, then, find the sum of the perimeter of both rectangles (in cm)?

The sum of the area of two rectangles is 384 cm2 and the breadth of both rectangles is equal to the diameter of the circle whose area is 16π cm2. If the difference between the lengths of both rectangles is 24 cm, then, find the sum of the perimeter of both rectangles (in cm)? Correct Answer 128

Given:

Sum of area of both rectangle = 384 cm2

Breadth of both rectangle = Diameter of the circle

Sum of length of both rectangle = 48 cm

Formula Used:

Area of rectangle = length × breadth

Perimeter of Rectangle = 2(length + breadth)

Area of circle = πr2

Perimeter of circle = 2πr

Calculation:

Suppose the length of both rectangle is x and y, respectively.

The area of the circle = πr2 = 16π

⇒ r2 = 16

⇒ r = 4 cm

The diameter of circle = 8 cm which is equal to breadth of the rectangle.

Sum of the area of both rectangle = 384 cm2

⇒ 8x + 8y = 384

⇒ x + y = 48 cm      ---(i)

Now, the difference between the lengths of the both rectangles = 24 cm

⇒ x – y = 24 cm      ---(ii)

Add both equation (i) and (ii), we have –

⇒ 2x = 72

⇒ x = 72/2

⇒ x = 36 cm

Put this value in the equation (i), we have –

⇒ 36 + y = 48

⇒ y = 12 cm

Therefore, perimeter of the first rectangle = 2(x + 8) = 2(36 + 8)

⇒ 2(44)

⇒ 88 cm

Perimeter of the second rectangle = 2(y +8)

⇒ 2(12 + 8)

⇒ 2(20)

⇒ 40 cm

The sum of the perimeter of both rectangle = (88 + 40) cm

⇒ 128 cm

Related Questions

Sum of perimeter of two rectangles is 248 cm and breadth of both rectangles is equal to radius of circle whose circumference is 44 cm. If length of both rectangles is in the ratio of 9 : 13, then find the difference between areas of both rectangles?
Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: A circle whose radius is 56 cm and The Rectangle whose length and breadth are in the ratio 7 ∶ 22 respectively. The area of a circle is equal to the area of a rectangle then calculate the perimeter of the rectangle. Quantity II: A cylinder whose radius is (1/7) of the radius of the circle and the height of the cylinder is twice the radius of the circle and the area of the circle is 154 cm2 then, find the volume of the cylinder.
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
If the area of the square and circle is 1406.25 cm2 and 1386 cm2, respectively. Then, how many tiles whose length and breadth are 66 cm and 20 cm, respectively will be need fit in a rectangle region whose length is equal to the perimeter of the circle and the breadth is equal to the perimeter of the square?
Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: Total surface area of a cylinder whose radius is 9 cm and height is equal to the side of a square of area 361 cm2. Quantity B: Area of a rectangle whose sides are in the ratio 5 : 4 and the perimeter is 2.5 times the perimeter of a semi-circle with area 308 cm2.
The total area of a rectangle and a circle is 3970 cm2. The radius of the circle is equal to the semi perimeter of the triangle. The perimeter of the triangle is 70 cm and the length of the rectangle is 3/7th of the radius of the circle.  Then, what is the ratio of the perimeter of the rectangle to the perimeter of the circle?
Which of the following statements is/are true? A: In a circle, PQ is a chord and OP and OQ are the radii of the circle. If ∠POQ = 90°, then ratio of the area of triangle POQ and that of circle will be 7: 22. B: Area of a circle is one-fourth of the product of ‘π’ and square of diameter of circle. C: Diameter of a semi-circle is 38(8/9)% of its perimeter.
The question below is followed by three statements I, II and III. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. What is the ratio of the volume of the cube to the volume of the cuboid? Statement I: The Total Surface Area of the cuboid is 550 cm2 and the ratio of the length, breadth and height of the cuboid is 2 : 3 : 1. Statement II: The Total Surface Area of the cube is 384 cm2. Statement III: The breadth of the cuboid is 1.5 times of the length of the cuboid and 3 times of the height of the cuboid. The difference between the height and the length of the cuboid is 5 cm.
Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.
Circle A is 4 cm in diameter; circle B is 5 cm in diameter, Circle C has its circumference equal to the sum of the circumferences of both A and B together, What will be the ratio of the area of circle C, with respect to the area of circle A and circle B respectively?