In a right angle triangle, the length of the longest side is given 450cm and one of its shortest side is 270cm . What is the length of its third side?
In a right angle triangle, the longest side is called the hypotenuse, and the other two sides are called the legs. Using the Pythagorean theorem, we can find the length of the third side (the other leg).
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Let "a" be the length of the first leg (270cm) and "c" be the length of the hypotenuse (450cm). Let "b" be the length of the other leg (which we need to find).
According to the Pythagorean theorem: a^2 + b^2 = c^2
Substituting the known values: 270^2 + b^2 = 450^2
72900 + b^2 = 202500
b^2 = 202500 - 72900
b^2 = 129600
Taking the square root of both sides: b = √129600
b ≈ 360
Therefore, the length of the third side is approximately 360cm.