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The width of a rectangle is 2 units less than the length. The area of the

rectangle is 48 square units. What is the width, in units, of the rectangle?

User Radders
by
8.3k points

1 Answer

4 votes

Answer:

6 units

Explanation:

Let's call the length of the rectangle "L" and the width "W".

From the problem, we know that the width is 2 units less than the length, so we can write:

W = L - 2

We also know that the area of the rectangle is 48 square units, so we can write:

A = L * W

Substituting the first equation into the second equation, we get:

48 = L * (L - 2)

Expanding the brackets, we get:

48 = L^2 - 2L

Rearranging, we get:

L^2 - 2L - 48 = 0

Now we can use the quadratic formula to solve for L:

L = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -2, and c = -48. Substituting these values into the formula, we get:

L = (2 ± sqrt(4 + 192)) / 2

L = (2 ± sqrt(196)) / 2

L = (2 ± 14) / 2

So, L = 8 or L = -6. We can ignore the negative solution, so the length of the rectangle is 8 units.

Now we can use the first equation to find the width:

W = L - 2

W = 8 - 2

W = 6

Therefore, the width of the rectangle is 6 units.

User SooCheng Koh
by
7.9k points

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