5. A square blanket is cut along its diagonal into two right triangle pieces. The hypotenuse of each piece has a length of 4 feet.
What are the lengths of the legs of each triangle piece?
Since each triangle is a right triangle and the hypotenuse has a length of 4 feet, we can use the Pythagorean theorem to find the lengths of the legs.
Let's call the length of each leg x.
According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
So, using this theorem, we have:
x^2 + x^2 = 4^2
2x^2 = 16
Divide both sides by 2:
x^2 = 8
Taking the square root of both sides:
x = √8 = 2√2
Therefore, the lengths of the legs of each triangle piece are 2√2 feet.