Question

The hypotenuse of right triangle is 25 CM and it's perpendicular distance is 7 CM, find the length of it's base.

Answer 1

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:

`b^2+7^2=25^2`

Solve the equation for b:

`\begin{gathered} \Rightarrow b^2=25^2-7^2=625-49 \\ \Rightarrow b^2=576 \\ \Rightarrow b=√(576)=24 \end{gathered}`

The length of the base is 24cm.