Final answer:
An isosceles right triangle with 4 cm leg lengths has a length of the altitude drawn from the right angle to the hypotenuse of approximately 5.66 cm.
Step-by-step explanation:
An isosceles right triangle has two legs of equal length. In this case, each leg measures 4 centimeters. To find the length of the altitude drawn from the right angle to the hypotenuse, we can use the relationship between the sides of a right triangle.
Since the legs of the triangle are equal, each leg measures 4 centimeters. Let's use 'l' to represent the length of the leg. Using the Pythagorean theorem, we have:
l2 + l2 = h2
Simplifying the equation, we get:2l2 = h2
To find the length of the altitude, we need to solve for 'h'. Since we know that each leg measures 4 centimeters, we can substitute 'l' with '4' in the equation and solve for 'h'. Let's do the calculations:
2(4)2 = h2
2(16) = h2
32 = h2
Taking the square root of both sides, we find:h ≈ 5.66 cm
Therefore, the length of the altitude drawn from the right angle to the hypotenuse is approximately 5.66 cm.
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