Question

A rectangular shaped park is 15 miles long and 8 miles wide. A diagonal path across the park is 17 miles long. Which of the following could be used to prove that the path through the park divides it into two

right triangles?
a. 152 - 82 = 172
b. 82 - 152 = 172
c. 82 + 172 = 152
d. 172-82 = 152

Answer 1

To prove that the diagonal path through a rectangular park creates two right triangles, the Pythagorean theorem is used, and the correct equation is 15^2 + 8^2 = 17^2.

Step-by-step explanation:

The question involves the use of the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is often written as a2 + b2 = c2. To prove that the diagonal path through the park creates two right triangles, we would need to show that the lengths of the sides of the park and the diagonal conform to this theorem.

In this case, the park is 15 miles long (length) and 8 miles wide (width), with a diagonal of 17 miles. The equation that would show the relationship between these measurements is a2 + b2 = c2, where a is the length, b is the width, and c is the diagonal. Therefore, the correct equation would be 152 + 82 = 172, which matches option a.