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<h2>Answer:</h2>
<em> The side of the triangle is either 38.63ft or 10.35ft</em>
<h2>Step-by-step explanation:</h2>This problem can be translated as an image as shown in the Figure below. We know that:
- The side of the square is 10 ft.
- One of the vertices of an equilateral triangle is on the vertex of a square.
- Two other vertices are on the not adjacent sides of the same square.
Let's call:
Since the given triangle is equilateral, each side measures the same length. So:
x: The side of the equilateral triangle (Triangle 1)
y: A side of another triangle called Triangle 2.
That length is the hypotenuse of other triangle called Triangle 2. Therefore, by Pythagorean theorem:
We have another triangle, called Triangle 3, and given that the side of the square is 10ft, then it is true that:
Therefore, for Triangle 3, we have that by Pythagorean theorem:
Matching equations (1) and (2):
Using quadratic formula:
Finding x from (1):
<em>Finally, the side of the triangle is either 38.63ft or 10.35ft</em>