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The perimeter of a rectangle is 54. The length is 9 more than 2 times the width. Find the width and length.

User Moriesta
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4 votes

Answer:

Let's denote the width of the rectangle as "w" and the length as "l."

According to the given information:

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, it is given as 54. So, we can write the equation:

2w + 2l = 54 (since a rectangle has two pairs of equal sides)

The length is 9 more than 2 times the width. Mathematically, this can be expressed as:

l = 2w + 9

Explanation:

Step 1: Substitute the value of l from equation 2 into equation 1.

2w + 2(2w + 9) = 54

Step 2: Simplify the equation by performing the multiplication.

2w + 4w + 18 = 54

Step 3: Combine like terms.

6w + 18 = 54

Step 4: Subtract 18 from both sides of the equation.

6w = 54 - 18

6w = 36

Step 5: Divide both sides of the equation by 6.

w = 36 / 6

w = 6

Now we have the width of the rectangle, which is 6.

Step 6: Substitute the value of w into equation 2 to find the length.

l = 2w + 9

l = 2(6) + 9

l = 12 + 9

l = 21

So, the width of the rectangle is 6 units, and the length is 21 units.

User Kms
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8.1k points

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