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The area of a rectangle is 4 times of the area of a square. The length of the rectangle is 90 cm and the breadth of the rectangle is 2/3 rd of the side of the square. What is the side of the square?

A) 10 cm
B) 20 cm
C) 15 cm
D) Couldn't be determined

Correct Answer:



C) 15 cm

Description for Correct answer:
Let the side of the square be x.

Breadth of the rectangle =\( \Large \frac{2}{3}x \)

According to the question.

=> \( \Large 90\times 2/3 x = 4x^{2}\)

x = \( \Large 90\times 2/3\times 1/4 \)=15 cm

Part of solved Area and perimeter questions and answers : >> Elementary Mathematics >> Area and perimeter

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Similar Questions

1). The area of a rectangle is 4 times of the area of a square. The length of the rectangle is 90 cm and the breadth of the rectangle is 2/3 rd of the side of the square. What is the side of the square?

A). 10 cm

B). 20 cm

C). 9 cm

D). Cannot be determined

2). The circumference of a circle is equal to the perimeter of a rectangle. The length and the breadth of the rectangle are 45 cm and 43 cm, respectively. What is the half the radius of the circle?

A). 56 cm

B). 14 cm

C). 28 cm

D). 15 cm

3). If the area of a circle is equal to the area of square with side \( \Large \Large 2\sqrt{\pi} \) units, what is the diameter of the circle ?

A). 1 unit

B). 2 units

C). 4 units

D). 8 units

4). If the circumference of a circle is equal to the perimeter of square, then which one of the following is correct?

A). Area of circle = Area of square

B). \( \Large Area \ of \ circle \ge \ Area \ of \ square \)

C). Area of circle > Area of square

D). Area of circle < Area of square

5). Consider the following statements.
The area of square is greater than the area of the triangle.
The area of circle is less than the area of triangle.
Which of the statement is/are correct?

A). Only I

B). Only II

C). Both l and II

D). Neither I nor II

6). ABCD is a rectangle. Let E be a point on AB and F a point on CD such that DE is parallel to BF.If AE = 3 cm and if the area of \( \Large \triangle BFC \) = 6 sq cm.
Consider the following statements.
Area of rectangle ABCD can be of the form \( \Large pq^{2} \) sq cm, where p, q are distinct primes.
Area of the figure EBFD is of the form \( \Large r^{2} \)sq cm, where r is rational but 5 not an integer.
Which of the above statements is/are correct?

A). Only I

B). Only II

C). Both l and II

D). Neither I nor II

7). What is the area between a square of side 10 cm and two inverted semi-circular, cross-sections each of radius 5 cm inscribed in the square?

A). \( \Large 17.5 cm^{2} \)

B). \( \Large 18.5 cm^{2} \)

C). \( \Large 20.5 cm^{2} \)

D). \( \Large 21.5 cm^{2} \)

8). The diameters of two circles are the side of a square and the diagonal of the square. The ratio of the areas of the smaller circle and the larger circle is

A). 1 : 4

B). \( \Large \sqrt{2}:\sqrt{3} \)

C). \( \Large 1:\sqrt{2} \)

D). 1 : 2

9). A regular hexagon is inscribed in a circle of radius 5 cm. If x is the area inside the circle but outside the regular hexagon, then which one of the following is correct where n is positive real number?

A). \( \Large 12 cm^{2} < x < 15 cm^{2} \)

B). \( \Large 15 cm^{2} < x < 17 cm^{2} \)

C). \( \Large 17 cm^{2} < x < 19 cm^{2} \)

D). \( \Large 19 cm^{2} < x < 21 cm^{2} \)

10). Which one of the following is a Pythagorean triple in which one side differs from the hypotenuse by two units?

A). \( \Large (2n+1,4n,2n^{2}+2n) \)

B). \( \Large (2n,4n,n^{2}+1) \)

C). \( \Large (2n^{2},2n,2n+1) \)

D). \( \Large (2n,n^{2}-1,n^{2}+1) \)