CTET Class I to V 2014 Sep Paper

Question : 44 of 150

Marks: +1, -0

Perimeters of a rectangle and a square are equal. Perimeter of the square is 96 cm and breadth of the rectangle is 4 cm less than the side of the square. Then two times the area (in square cm) of the rectangle is

560
960
1040
1120

Validate

Solution:

Let length of rectangle be

x {cm}

and breadth be

y {cm} .

Perimeter of a rectangle

=2(x+y)

Let side of a square

=a\; {cm}

Perimeter of a square

=4 a

Now, perimeter of square

=96 {cm}

⇒ \;\; 4 a=96

∴ a=24 {cm}

Breadth of a rectangle

(y)=24-4=20 {cm}

According to question

⇒ 2(x+20)=96

⇒ x+20=48

∴ x=48-20=28 {cm}

Area of rectangle

=28 × 20=560 {cm}^{2}

Two times of the area of rectangle

=2 × 560 {cm}^{2}

=1120 {cm}^{2}

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