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The length of a rectangle is 7 inches more than 3 times the width. If the area of the rectangle is 76 square inches, find the length and the width.

User Phs
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1 Answer

1 vote

Answer:

the length of the rectangle is 19 inches.

Explanation:

Let's start by setting up equations based on the information given.

Let L be the length and W be the width of the rectangle. We know that:

L = 3W + 7 (because the length is 7 inches more than 3 times the width)

Area of rectangle = LW = 76

Now we can substitute the first equation into the second equation to get:

(3W + 7)W = 76

Simplifying, we get:

3W^2 + 7W - 76 = 0

We can solve for W by using the quadratic formula:

W = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = 7, and c = -76. Plugging in these values, we get:

W = (-7 ± sqrt(7^2 - 4(3)(-76))) / 2(3)

W ≈ 4 or W ≈ -6.33

We can ignore the negative solution since the width cannot be negative. So the width of the rectangle is approximately 4 inches.

To find the length, we can use the first equation we set up:

L = 3W + 7

L = 3(4) + 7

L = 19

So the length of the rectangle is 19 inches.

User Thelouras
by
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