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A rectangle has a length of 13 inches less than 6 times its width. If the area of the rectangle is 6105 square inches, find the length of the rectangl

User LucaMus
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1 Answer

4 votes

Answer:

the length of the rectangle is 185 inches.

Explanation:

Let's denote the width of the rectangle as "w" (in inches) and the length of the rectangle as "L" (in inches).

Given that the length is 13 inches less than 6 times its width, we can write this as an equation:

L = 6w - 13

We are also given that the area of the rectangle is 6105 square inches:

Area = Length × Width

6105 = L × w

Substitute the expression for "L" from the first equation into the area equation:

6105 = (6w - 13) × w

Now, let's solve for "w":

6105 = 6w^2 - 13w

6w^2 - 13w - 6105 = 0

To solve this quadratic equation, you can use the quadratic formula:

w = (-b ± √(b^2 - 4ac)) / 2a

For this equation, a = 6, b = -13, and c = -6105. Plugging in these values:

w = (-(-13) ± √((-13)^2 - 4 × 6 × (-6105))) / (2 × 6)

w = (13 ± √(169 + 146520)) / 12

w = (13 ± √146689) / 12

Since we're dealing with measurements, the width can't be negative. So, taking the positive root:

w = (13 + 383) / 12

w = 396 / 12

w = 33

Now that we have the width, we can use the equation for the length:

L = 6w - 13

L = 6 × 33 - 13

L = 198 - 13

L = 185

User Stefan Haberl
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