The figure shows an isosceles right triangle with legs of equal length. If the hypotenuse measures 14√2 centimeters, what is the length of each leg?
- 14 centimeters using the relationship leg = hypotenuse ÷ √2 (correct answer)
- 7√2 centimeters by dividing the hypotenuse by 2
- 28 centimeters by multiplying hypotenuse by √2
- 10 centimeters using an approximation of √2 ≈ 1.4
Explanation: In an isosceles right triangle, if each leg has length s, then hypotenuse = s√2. Given hypotenuse = 14√2, we have s√2 = 14√2, so s = 14 cm. Choice B gives 7√2 ≈ 9.9 cm, which would make hypotenuse = √[(7√2)² + (7√2)²] = √[98 + 98] = 14, not 14√2. Choice C gives 28 cm, making hypotenuse = 28√2. Choice D uses approximation incorrectly.