To solve the given problem of finding the correct equation that can be used to determine the dimensions of the patio, we need to break down the problem step-by-step and use geometric principles.
1. Identify Variables:
- Let's denote the width of the rectangular patio by [tex]\(x\)[/tex] meters.
- The length of the patio, being 5 meters more than the width, is [tex]\(x + 5\)[/tex] meters.
2. Determine the Relationship:
- The diagonal path across the patio forms the hypotenuse of a right triangle, where the width [tex]\(x\)[/tex] and the length [tex]\(x + 5\)[/tex] are the legs of the triangle.
3. Apply the Pythagorean Theorem:
- The Pythagorean theorem states that for a right triangle with legs [tex]\(a\)[/tex] and [tex]\(b\)[/tex], and hypotenuse [tex]\(c\)[/tex], the relationship is given by [tex]\(a^2 + b^2 = c^2\)[/tex].
- Here, the width [tex]\(x\)[/tex] and the length [tex]\(x + 5\)[/tex] are the legs, and the diagonal path of the patio, which is 29 meters, is the hypotenuse.
4. Formulate the Equation:
- According to the Pythagorean theorem:
[tex]\[
x^2 + (x + 5)^2 = 29^2
\][/tex]
5. Simplify the Right Side:
- Calculate [tex]\(29^2\)[/tex]:
[tex]\[
29^2 = 841
\][/tex]
6. Write the Final Equation:
- Plugging in the value, the correct equation is:
[tex]\[
x^2 + (x + 5)^2 = 841
\][/tex]
So, the correct equation that can be used to find the dimensions of the patio is:
[tex]\[
x^2 + (x + 5)^2 = 841
\][/tex]
