Question

pre-algebra ic sem 2 fall 2025
square roots and right
triangles
which equation can be used to find the unknown length, b, in this triangle?
4² + b² = 5²
5² + 4² = b²
5² + b² = 4²
4² - b² = 5²

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the legs.

Step2: Identify the sides

In the given right - triangle, the hypotenuse \(c = 5\) in (the longest side), one leg \(a=4\) in, and the other leg is \(b\).

Step3: Substitute into the Pythagorean theorem

Substituting \(a = 4\) and \(c = 5\) into \(a^{2}+b^{2}=c^{2}\), we get \(4^{2}+b^{2}=5^{2}\)

Answer:

\(4^{2}+b^{2}=5^{2}\)