To find the dimensions of the rectangular deck, we can set up an equation based on the information provided.
Let’s denote the width of the deck as x. According to the question, the length of the deck is 5 feet longer than its width. Therefore, we can express the length as (x + 5).
The area of a rectangle is calculated by multiplying its length by its width. Therefore, we have the following equation:
x * (x + 5) = 310
Expanding this, we get:
x² + 5x – 310 = 0
This is a standard quadratic equation. To solve for x, we can factor the equation or use the quadratic formula. First, we will try factoring:
We are looking for two numbers that multiply to -310 and add up to 5. The numbers 20 and -15 fit this requirement.
So, we can factor the equation as:
(x + 20)(x – 15) = 0
This gives us two possible solutions:
- x + 20 = 0 → x = -20 (not a valid solution since width cannot be negative)
- x – 15 = 0 → x = 15
Since x is the width, we have:
- Width = x = 15 feet
- Length = x + 5 = 15 + 5 = 20 feet
Thus, the dimensions of the deck are:
- Width: 15 feet
- Length: 20 feet
This means the rectangular deck has a width of 15 feet and a length of 20 feet, which gives an area of 310 square feet as required.