Question

which of the following scenarios can be solved using the pythagorean theorem?
a. calculating the area of a circle
b. determining the length of a ladder needed to reach a certain height
c. finding the circumference of a rectangle
d. measuring the volume of a cube

Explanation:

Step1: Understand the Pythagorean Theorem

The Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of a right - triangle and \(c\) is the hypotenuse.

Step2: Analyze each option

• Option a: The area of a circle is \(A = \pi r^{2}\), which has nothing to do with the Pythagorean Theorem.
• Option b: When a ladder leans against a wall, the wall height (\(a\)), the distance from the base of the wall to the base of the ladder (\(b\)), and the length of the ladder (\(c\)) form a right - triangle. So, \(c=\sqrt{a^{2}+b^{2}}\) (using the Pythagorean Theorem).
• Option c: The circumference of a rectangle (perimeter \(P=2(l + w)\)) is not related to the Pythagorean Theorem.
• Option d: The volume of a cube \(V=s^{3}\) is not related to the Pythagorean Theorem.

Answer:

B. Determining the length of a ladder needed to reach a certain height