Question

If one side of an isosceles right triangle is \( 5\sqrt{2} \) cm, then the length of its hypotenuse is:

• A. 10 cm
• B. \( 10\sqrt{2} \) cm
• C. 15 cm
• D. \( 15\sqrt{2} \) cm

Hint:

In an isosceles right triangle, the hypotenuse is \( \sqrt{2} \) times the length of a leg.

Answer 1

The Correct Option is B

In an isosceles right triangle, the two legs are equal, and the relationship between the legs and the hypotenuse is given by the Pythagorean theorem: \[ \text{Hypotenuse}^2 = \text{Leg}^2 + \text{Leg}^2 = 2 \times \text{Leg}^2 \] Let the length of each leg be \( a = 5\sqrt{2} \) cm.
Step 1: Apply the Pythagorean theorem.
The hypotenuse \( c \) is: \[ c^2 = 2 \times (5\sqrt{2})^2 \]
Step 2: Simplify the equation.
\[ c^2 = 2 \times 25 \times 2 = 100 \] \[ c = \sqrt{100} = 10\sqrt{2} \]
Step 3: Conclusion.
Therefore, the length of the hypotenuse is \( 10\sqrt{2} \) cm.