To find the area of the square inside the right triangle, we use the relationship between the dimensions of the right triangle and the square.
The triangle has side lengths 3, 4, and 5, confirming it's a Pythagorean triple. The base and height are 3 and 4, and the hypotenuse is 5.
Let the side of the square be \( s \). The formula to find \( s \) for a square inscribed in a right triangle is:
\( s = \frac{ab}{a + b + c} \)
Where \( a = 3 \), \( b = 4 \), and \( c = 5 \).
So:
\( s = \frac{3 \times 4}{3 + 4 + 5} = \frac{12}{12} = 1 \).
The area of the square is:
\( \text{Area} = s^2 = 1^2 = 1 \).
The area of the square is 1 square unit.
#MathPuzzle #RightTriangle #Geometry
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1moLooking good, Jacob Harmon!