Questions: Meosha eyes a small rectangular lot for sale. The perimeter of the yard is 252 feet. The width of the lot is 26 feet shorter than the length. What are the dimensions of the lot? Submit your answer as an ordered pair (x, y) without spaces. If there is more than one solution, enter (x, mx-b) where m and b are integers. If there is no solution, write: No Solution.

Solution Steps

To find the dimensions of a rectangle when given the perimeter and the relationship between length and width, express the width in terms of the length using the given relationship, substitute this expression into the perimeter formula to get an equation with one variable, solve for the length, and then use the length to find the width.

Let the length of the lot be \( x \) feet. According to the problem, the width of the lot is 26 feet shorter than the length. Therefore, the width can be expressed as: \[ \text{width} = x - 26 \]

The perimeter of a rectangle is given by: \[ P = 2(\text{length} + \text{width}) \] Given that the perimeter is 252 feet, we can substitute the expressions for length and width: \[ 252 = 2(x + (x - 26)) \]

Simplify the equation to solve for \( x \): \[ 252 = 2(2x - 26) \\ 252 = 4x - 52 \\ 252 + 52 = 4x \\ 304 = 4x \\ x = \frac{304}{4} \\ x = 76 \]

Now that we have the length \( x = 76 \) feet, we can find the width: \[ \text{width} = 76 - 26 = 50 \]

Final Answer