Answer: A

In an isosceles right triangle, the hypotenuse is $\sqrt{2}$ times the length of a leg, so the hypotenuse is $7\sqrt{2} \times \sqrt{2} = 7 \times 2 = 14$. The Pythagorean theorem confirms it: $(7\sqrt{2})^2 + (7\sqrt{2})^2 = 98 + 98 = 196$, and $\sqrt{196} = 14$.

Choice D is the square of the hypotenuse; the Pythagorean theorem gives $c^2 = 196$, so $c = 14$.

Why the other choices are wrong

• B. This doubles the leg. The hypotenuse is the leg times the square root of 2.
• C. 98 is the square of one leg, not the hypotenuse.
• D. 196 is the square of the hypotenuse. Take the square root.