A right triangle has a hypotenuse of $14$ units and one leg of $7$ units. What is the length of the other leg?

• A. $7$ units
• B. $\sqrt{147}$ units
• C. $\sqrt{49}$ units
• D. $14$ units

Answer: (B)

Verified step by step guidance

1. Identify the sides of the right triangle: the hypotenuse \(c = 14\) units, one leg \(a = 7\) units, and the unknown leg \(b\).
2. Recall the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse: \(a^2 + b^2 = c^2\).
3. Substitute the known values into the Pythagorean theorem: \$7^2 + b^2 = 14^2$.
4. Calculate the squares of the known sides: \$49 + b^2 = 196$.
5. Isolate \(b^2\) by subtracting 49 from both sides: \(b^2 = 196 - 49\), then express \(b\) as \(b = \sqrt{196 - 49}\) to find the length of the other leg.