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Question 1209519: (38) Find the value of w.
Link to diagram: https://ibb.co/202BWZT9
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! In a square, the diagonal divides the square into two right-angled triangles. The sides of the square form the legs of the right triangle, and the diagonal is the hypotenuse.
We can use the Pythagorean theorem to find the length of the diagonal (w). The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): a² + b² = c²
In this case, the sides of the square are a = 10 and b = 10, and the diagonal is c = w. So:
10² + 10² = w²
100 + 100 = w²
200 = w²
To find w, we take the square root of both sides:
w = √200
w = √(100 * 2)
w = 10√2
Therefore, the length of the diagonal (w) is 10√2.
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