Question

a project designs a diagonal path across a rectangular patio. the path is 29 meters long. the width of the patio is x meters, and the length of the path is 5 meters more than the width. which equation can be used to find the dimensions of the patio? 0.5(x)(x + 5) = 29 0.5(x)(x + 5) = 841 x² + (x + 5)² = 29 x² + (x + 5)² = 841

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). In a rectangle, the diagonal forms a right - triangle with the length and width of the rectangle. Here, \(a = x\), \(b=x + 5\), and \(c = 29\).

Step2: Substitute values into the theorem

Substituting the values into the Pythagorean theorem formula, we get \(x^{2}+(x + 5)^{2}=29^{2}\).
Since \(29^{2}=841\), the equation becomes \(x^{2}+(x + 5)^{2}=841\).

Answer:

\(x^{2}+(x + 5)^{2}=841\) (the fourth option)