Question

Write an equation that models the relationship between the lengths of the two legs and the hypotenuse.

a. da = f + e?
b. fp = e? - de
c. f² = e? + d?
d. e² = f + d²

Answer 1

The Pythagorean theorem, expressed as f² = e² + d², accurately represents the relationship between the lengths of the legs (e and d) and the hypotenuse (f) of a right triangle.

Step-by-step explanation:

The correct equation that models the relationship between the lengths of the two legs and the hypotenuse of a right triangle is the Pythagorean theorem. Given the lengths of the legs labeled e and d, and the hypotenuse labeled f, the Pythagorean theorem states that:

f² = e² + d²

This can be further expanded to solve for f, the length of the hypotenuse, by taking the square root of both sides:

f = √(e² + d²)

This relationship is fundamental in mathematics to determine the straight-line distance in right-angled scenarios, such as in navigation or geometry problems.