To solve the puzzle, find x in the equation.
1: the hypotenuse is 77cm and the other length is 36cm.
2: the hypotenuse is 80cm and the other length is 39cm
what is the third length, x?
To solve for the third length, x, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
1. Using the Pythagorean theorem, we have:
x^2 + 36^2 = 77^2
Simplifying this equation, we get:
x^2 + 1296 = 5929
Subtracting 1296 from both sides, we have:
x^2 = 4633
Taking the square root of both sides, we find:
x ≈ 68.08 cm
Therefore, the length of the third side, x, is approximately 68.08 cm.
2. Similarly, using the Pythagorean theorem, we have:
x^2 + 39^2 = 80^2
Simplifying this equation, we get:
x^2 + 1521 = 6400
Subtracting 1521 from both sides, we have:
x^2 = 4879
Taking the square root of both sides, we find:
x ≈ 69.89 cm
Therefore, the length of the third side, x, is approximately 69.89 cm.