If a right-angled triangle has a hypotenuse of cm, and the length of one of its sides is cm, determine the length of the remaining side using factorization.
Use Pythagoras' theorem, which states that the square of the length of a right-angled triangle's hypotenuse
is equal to the sum of the squares of the lengths of the other two sides.
Let represent the length of the remaining side, and solve for .
Remember that the difference of two squares can be factorised using this rule:
Note that we only use the positive value of the square root below, because it would not make sense to have a side length with a negative value.
So, the length of the remaining side is cm.