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A rectangular piece of metal has a perimeter of 20 centimeters. It’s area is 24 centimeters. What are the dimensions of the piece

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Answer:

Explanation:

Let's use the formula for the perimeter of a rectangle: P = 2L + 2W, where L is the length and W is the width.

We are given that the perimeter is 20 cm, so:

20 = 2L + 2W

Simplifying this equation, we get:

10 = L + W

We are also given that the area of the rectangle is 24 cm, so:

24 = LW

Now we have two equations with two variables, which we can solve using substitution. Solving the first equation for L, we get:

L = 10 - W

Substituting this expression for L into the second equation, we get:

24 = (10 - W)W

Expanding the brackets and rearranging, we get a quadratic equation:

W^2 - 10W + 24 = 0

We can factor this equation as:

(W - 6)(W - 4) = 0

So the possible values for W are 6 cm and 4 cm. To find the corresponding values for L, we can use the equation L = 10 - W:

If W = 6, then L = 4

If W = 4, then L = 6

Therefore, the dimensions of the piece of metal are 4 cm by 6 cm.

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