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Mathematics

If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

Polynomials

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Answer

Let the width of the rectangle be x cm.

Then, the length of the rectangle = (2x + 3) cm.

Perimeter of a rectangle = 2(length + width)

According to the question, the perimeter is 24 cm.

So,

2[(2x + 3) + x] = 24

⇒ 2[3x + 3] = 24

⇒ 6x + 6 = 24

⇒ 6x = 24 - 6

⇒ 6x = 18

⇒ x = 186\dfrac{18}{6}

⇒ x = 3

So,

Width of the rectangle = 3 cm

Length of the rectangle = 2(3) + 3 = 6 + 3 = 9 cm

Hence, the dimensions of the rectangle are: length = 9 cm and width = 3 cm.

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