Question

an architect 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

In a right - triangle (formed by the length, width, and diagonal of the rectangle), the Pythagorean theorem states that \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse. Here, \(a = x\), \(b=x + 5\), and \(c = 29\).
So, \(x^{2}+(x + 5)^{2}=29^{2}\).

Step2: Calculate \(29^{2}\)

We know that \(29^{2}=841\).

Answer:

D. \(x^{2}+(x + 5)^{2}=841\)