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If the length of a rectangle is three more than triple the width, and the perimeter of the rectangle is 110 units, what are the dimensions of the rectangle?

A. Length = 33 units, Width = 11 units
B. Length = 22 units, Width = 16 units
C. Length = 25 units, Width = 20 units
D. Length = 28 units, Width = 18 units

User Simon Lee
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1 Answer

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Final answer:

To find the dimensions of the rectangle, we need to set up a system of equations based on the given information. By solving the system, we find that the length of the rectangle is 42 units and the width is 13 units.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations based on the given information. Let's assume that the width of the rectangle is x units. According to the problem statement, the length of the rectangle is 3 more than triple the width, so it can be expressed as 3x + 3 units.

The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the expressions for length and width into the formula, we get 110 = 2(3x + 3 + x). Simplifying the equation, we have 110 = 2(4x + 3). Multiplying out the parenthesis, we get 110 = 8x + 6. Subtracting 6 from both sides, we have 104 = 8x. Dividing both sides by 8, we find that x = 13. Substituting this value back into the expression for length, we get length = 3(13) + 3 = 42 units. Therefore, the dimensions of the rectangle are Length = 42 units and Width = 13 units.

User Aakash Dave
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