The legs of a right triangle are (x) cm and (x+18) cm and the hypotenuse is (90) cm. What is the smaller leg?

Correct answer: (54) cm

The direct answer is option B, 54 cm. By the Pythagorean theorem, x^2+(x+18)^2=90^2. Expanding gives 2x^2+36x+324=8100, so x^2+18x-3888=0. Factoring gives (x-54)(x+72)=0. A length cannot be negative, so x=54. The other leg is 72, and 54^2+72^2=90^2, confirming the answer. Option A, 48, would pair with 66 and fails the theorem. Option B, 54, pairs with 72 and works exactly. Option C, 60, would pair with 78 and gives a sum of squares larger than 90^2. Option D, 72, is the larger leg, not the smaller one; it also makes x+18=90 if treated as x, which is inconsistent with the required pair. Exam cue: use the hypotenuse as the largest side and discard the negative algebraic root because lengths are positive.