Using the Pythagorean Theorem, the length of the shorter leg is 12√2 in.
The problem can be solved using Pythagorean or Pythagoras Theorem.
Pythagorean Theorem states that in a right-angled triangle, the square of the longest side ( hypotenuse ) is equal to the sum of the squares of the other shorter sides.
It is often expressed as:
c² = a² + b²
The triangle given in the problem has angles: 45⁰, 45⁰, 90⁰.
Therefore, it is an isosceles right triangle.
Substitute the given parameters to the Pythagoras equation:
c = 24 in.
a² + b² = 24²
But a = b, therefore,
a² + a² = 24²
2a² = 24²
a² = 24²/2 = (2 x 12)²/2
a² = 2 x 12²
a = 12√2 inches.
Read more about the Pythagorean Theorem here:
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