Final answer:
To determine the length of the longer side of the rectangle, the Pythagorean theorem is used. We denote the shorter side as x, so the longer side is x + 7 inches. After solving the quadratic equation, we find that the length of the longer side is 15 inches.
Step-by-step explanation:
To find the length of the longer side of the rectangle, we will use the Pythagorean theorem. Let's call the shorter side of the rectangle x inches. Hence, the longer side would be x + 7 inches, because one side is 7 inches longer than the other according to the question. The diagonal divides the rectangle into two right triangles, so we can write the equation as:
x^2 + (x + 7)^2 = 17^2
By solving this equation, we'll find the value of x and consequently x + 7. Here are the calculation steps:
- x^2 + (x + 7)^2 = 17^2
- x^2 + x^2 + 14x + 49 = 289
- 2x^2 + 14x + 49 = 289
- 2x^2 + 14x - 240 = 0
- This quadratic equation can be factored or solved using the quadratic formula. In this case, factorization gives us two possible values for x, but only one of them will be a positive and practical dimension.
- x = 8, which means the longer side is x + 7 = 15 inches.
Therefore, the length of the longer side of the rectangle is 15 inches.