In a right triangle, one leg measures $8\mathrm{cm}$ and the hypotenuse measures $16\mathrm{cm}$. What is the length of the other leg?

• A. $20\mathrm{cm}$
• B. $8\mathrm{cm}$
• C. $40\mathrm{cm}$
• D. $14\mathrm{cm}$

Answer: (D)

Verified step by step guidance

1. Identify the given elements in the right triangle: one leg measures 8 cm and the hypotenuse measures 16 cm.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b): \(c^2 = a^2 + b^2\).
3. Assign the known values: let the known leg be \(a = 8\) cm, the hypotenuse be \(c = 16\) cm, and the unknown leg be \(b\) cm.
4. Set up the equation using the Pythagorean theorem: \$16^2 = 8^2 + b^2$.
5. Solve for \(b^2\) by subtracting \$8^2\( from both sides: \)b^2 = 16^2 - 8^2\(. Then, find \)b\( by taking the square root of \)b^2$.