To solve the problem, we need to analyze the relationship between the hypotenuse and the legs of the right isosceles triangles in the pinwheel design.
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Understanding the right isosceles triangle: In a right isosceles triangle, the two legs are the same length, and the relationship between the legs and the hypotenuse is given by the Pythagorean theorem: \[ c = \sqrt{a^2 + a^2} = a\sqrt{2} \] where \( c \) is the hypotenuse and \( a \) is the length of each leg.
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Given information: Each triangle has a hypotenuse of 5 inches.
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Finding the legs:
- Using the relationship we derived: \[ 5 = a\sqrt{2} \]
- Solving for \( a \): \[ a = \frac{5}{\sqrt{2}} = \frac{5\sqrt{2}}{2} \]
- This value approximates to about \( 3.54 \) inches when calculated, but we will leave it in the exact form for select purposes.
Now we can fill in the blanks:
- Query 1: Each triangle in the design is a right triangle.
- Query 2: The legs of each triangle are \(\frac{5\sqrt{2}}{2}\) inches long. If asked for a decimal result, you could alternatively provide that as approximately 3.54 inches.
Thus the final statements will be:
- Each triangle in the design is a right triangle.
- Because the length of the hypotenuse of each triangle is 5 inches long, the legs of each triangle are approximately 3.54 inches long (or left as \(\frac{5\sqrt{2}}{2}\) for an exact value).
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