The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm.What is the smallest possible whole-number value of x?

For the triangle to be acute, the square of its longest side must be less than the sum of the squares of the other two sides: 15² < x² + (2x)² = 5x². This gives x > √45, or about 6.71. The smallest whole number that works is 7; its sides are 7, 14, and 15, so 15 is still the longest side.

AI-written and checked against the verified answer.