The hypotenuse of a right triangle is given to be 25cm and its perpendicular distance is 7cm. It is required to find the length of the base(b).
A sketch is shown below:
Apply the Pythagorean Theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of its perpendicular and base.
It follows from the theorem that:
[tex]b^2+7^2=25^2[/tex]
Solve the equation for b:
[tex]\begin{gathered} \Rightarrow b^2=25^2-7^2=625-49 \\ \Rightarrow b^2=576 \\ \Rightarrow b=\sqrt{576}=24 \end{gathered}[/tex]
The length of the base is 24cm.
