Question

Find the exact length of the third side.
52
48

Answer 1

Here in diagram

• this is a Right angled triangle
• where
• hypontenuse =h=52
• Base=b=48

We need to find

• perpendicular =p

According to Pythagorean theory

`{\boxed{\sf h^2=p^2+b^2}}`

`\qquad\quad {:}\longrightarrow\tt p^2=h^2-b^2`

`\qquad\quad {:}\longrightarrow\tt p=\sqrt {h^2-b^2}`

• Substitute the values

`\qquad\quad {:}\longrightarrow\tt p=√(52^2-48^2)`

`\qquad\quad {:}\longrightarrow\tt p=\sqrt {2704-2304}`

`\qquad\quad {:}\longrightarrow\tt p=√(400)`

`\qquad\quad {:}\longrightarrow\tt p=20`