Given a right triangle QSU with side lengths $\mathrm{QS}=5$ units, $\mathrm{SU}=12$ units, and $\mathrm{UQ}$ as the hypotenuse, what is the perimeter of triangle QSU?

• A. $3$ units
• B. $30$ units
• C. $16$ units
• D. $40$ units

Answer: (B)

Verified step by step guidance

1. Identify the sides of the right triangle QSU: QS = 5 units, SU = 12 units, and UQ is the hypotenuse.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: \(UQ^2 = QS^2 + SU^2\).
3. Calculate the length of the hypotenuse UQ by substituting the known side lengths into the Pythagorean theorem: \(UQ^2 = 5^2 + 12^2\).
4. Simplify the expression to find \(UQ^2 = 25 + 144\), then take the square root of both sides to find \(UQ = \sqrt{169}\).
5. Once you have the length of UQ, find the perimeter of triangle QSU by adding all three side lengths: \(Perimeter = QS + SU + UQ\).