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The length of a rectangle is 5 m more than twice the width, and the area of the rectangle is 63 m². Find the dimensions of the rectangle.

Length=

Width =

The length of a rectangle is 5 m more than twice the width, and the area of the rectangle-example-1
User Uggeh
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1 Answer

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16 votes

Answer:

width = 9/2 m

length = 14 m

Explanation:

Let width = x

If the length of a rectangle is 5 m more than twice the width:

⇒ length = 2x + 5

Use the given information to create a quadratic equation:

Area of a rectangle = width × length

⇒ 63 = x(2x + 5)

⇒ 63 = 2x² + 5x

⇒ 2x² + 5x - 63 = 0

Find the value of x by factorizing the quadratic:

⇒ 2x² + 5x - 63 = 0

⇒ 2x² + 5x - 63 = 0

⇒ 2x² + 14x - 9x - 63 = 0

⇒ 2x(x + 7) - 9(x + 7) = 0

⇒ (2x - 9)(x + 7) = 0

Therefore:

⇒ (2x - 9) = 0 ⇒ x = 9/2

⇒ (x + 7) = 0 ⇒ x = -7

Width cannot be negative, therefore, x = 9/2 only

⇒ width = 9/2 m

⇒ length = 2(9/2) + 5 = 14 m

User JamieL
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