The area of a rectangular tabletop is 3 square meters. If the width is 0.5 m shorter than the length, what are the dimensions of the tabletop?

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The area of a rectangular tabletop is 3 square meters. If the width is 0.5 m shorter than the length, what are the dimensions of the tabletop?

Answer:

L = 2

W = 1.5

Solution:

Let L be the length and W be the width

Area of rectangle = LW

LW = 3

W = L – 0.5

Substitute L for W

L(L-0.5) = 3

Subtract 3 to both sides

L^2 - 0.5L - 3

Solve this using quadratic formula, where a = 1, b = -0.5 and c = -3

L=\frac{-(-0.5)±\sqrt{-0.5^2-4(1)(-3)} }{2(1)}

L = \frac{0.5±\sqrt{0.25+12} }{2}

L = \frac{0.5±3.5}{2}

We will ignore negative answer because there is no dimension that is a negative number.

L = 2

Since we already found the length, we can also find the width.

W = L – 0.5

W = 2 – 0.5 = 1.5

Therefore the dimensions are 2 and 1.5

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