To find the lengths of the legs of each right triangle piece derived from cutting a square blanket along its diagonal, we'll use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (\(c\)) is equal to the sum of the squares of the lengths of the other two sides (\(a\) and \(b\)). Since these legs are the sides of the original square and are equal in length, we know that:
\[ c^2 = a^2 + b^2 \]
Given that \(a = b\) (because they are the sides of a square), the equation simplifies to:
\[ c^2 = 2a^2 \]
We know the hypotenuse \(c\) is 4 feet:
\[ 4^2 = 2a^2 \]
\[ 16 = 2a^2 \]
Divide both sides by 2:
\[ a^2 = 8 \]
Take the square root of both sides to find \(a\):
\[ a = \sqrt{8} \]
\[ a = \sqrt{4 \times 2} \]
\[ a = 2 \sqrt{2} \]
Therefore, the lengths of the legs of each triangle piece are \(2\sqrt{2}\) feet.
A square blanket is cut along its diagonal into two right triangle pieces. The hypotenuse of each piece has a length of 4 feet.
What are the lengths of the legs of each triangle piece?
1 answer