Answer:To find the length of the hypotenuse of a right isosceles triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Given that the square has an area of 100 square feet, we can find the length of one side of the square by taking the square root of the area.
√(100) = 10 feet
Since the square is right isosceles, two sides of the square are equal in length. Therefore, each side of the square is 10 feet.
In a right isosceles triangle, the two legs are equal in length. So, the length of each leg of the triangle is also 10 feet.
Using the Pythagorean theorem, we can find the length of the hypotenuse. Let's denote the length of the hypotenuse as c.
c^2 = a^2 + b^2
Since the legs of the triangle are equal and have a length of 10 feet, we can substitute a = b = 10 into the equation.
c^2 = 10^2 + 10^2
c^2 = 100 + 100
c^2 = 200
To find the length of the hypotenuse, we take the square root of both sides.
c = √200
However, the square root of 200 is an irrational number. Therefore, the length of the hypotenuse cannot be expressed as a simple fraction or whole number.
In conclusion, the length of the hypotenuse of the right isosceles triangle cannot be expressed as a simple fraction or whole number and is approximately equal to √200.
Explanation: