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Question

What is the length and breadth of a rectangle if its perimeter is 12 cm and its length is 2 times its breadth?

A
4 cm, 2 cm
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B
2 cm, 1 cm
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C
6 cm, 3 cm
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D
7 cm, 4 cm
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Solution

The correct option is A 4 cm, 2 cm
Given that,
length=2×breadth
l=2b

We know that,
opposite sides of the rectangle are of equal length.

Perimeter of the rectangle
= Length of side AB + Length of side BC + Length of side CD + Length of side DA
= l+b+l+b
= 2l+2b
=2(l+b)
=2(2b+b) = 2(3b)= 6b

Now, perimeter of the rectangle = 12 cm

So, 6b=12 cm

Using trial and error method,

case 1:

putting b=1,
LHS = 6×1 = 6
Hence, LHS is not equal to RHS.

case 2:

putting b=2,
LHS = 6×2 = 12
Hence, LHS is equal to RHS.

breadth=2 cm
length=2×breadth
length=2×2 = 4 cm

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