Question

which of the following scenarios can be solved using the pythagorean theorem? a. determining the length of a ladder needed to reach a certain height b. measuring the volume of a cube c. finding the circumference of a rectangle d. calculating the area of a circle which statement accurately defines the pythagorean theorem? a. the square of the hypotenuse equals the sum of the squares of the base. b. the square of the hypotenuse equals the sum of the squares of the legs. c. the sum of the squares of the three sides equals the square of the perimeter. d. the sum of the squares of the two sides equals the square of the base.

Explanation:

First Question:

The Pythagorean Theorem is used for right - angled triangles. In the case of a ladder leaning against a wall, the ladder is the hypotenuse of a right - angled triangle, the height on the wall is one leg, and the distance from the base of the wall to the base of the ladder is the other leg. Measuring the volume of a cube uses the formula $V = s^3$, finding the circumference of a rectangle is $C=2(l + w)$ and calculating the area of a circle uses $A=\pi r^2$.

Second Question:

The Pythagorean Theorem states that in a right - angled triangle, if $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse, then $a^{2}+b^{2}=c^{2}$, which means the square of the hypotenuse equals the sum of the squares of the legs.

Answer:

1. A. Determining the length of a ladder needed to reach a certain height
2. B. The square of the hypotenuse equals the sum of the squares of the legs.