Final answer:
To find the length of the legs of an isosceles right triangle with a hypotenuse of 14, the Pythagorean theorem is used, revealing that each leg equals 7√2.
Step-by-step explanation:
To find the length of each leg of an isosceles right triangle with a hypotenuse of 14, we use the Pythagorean theorem. In an isosceles right triangle, the lengths of the two legs are equal, so we can denote them both as 'a'. According to the theorem: a² + a² = c², which simplifies to 2a² = c². Plugging in the length of the hypotenuse, the equation becomes 2a² = 14². When you solve for 'a', you get:
a² = ¢(14² / 2) = ¢(196 / 2) = ¢(98) = 7√2
Therefore, the length of each leg of the triangle is 7√2.