Given triangle is a right angled triangle with hypotenuse 25 units and altitude 24 units.
To find the length of the base, use the Pythagoras formula
[tex]\text{Hypotenuse}^2=Base^2+Altitude^2[/tex]
From the formula,
[tex]\text{Base}^2=Hypotenuse^2-Altitude^2[/tex]
Substitute the lengths of hypotenuse and altitude nto the formula.
[tex]\begin{gathered} \text{Base}^2=25^2-24^2 \\ =625-576 \\ =49 \end{gathered}[/tex]
Take square root on both sides.
[tex]\begin{gathered} \text{Base}=\sqrt[]{49} \\ =7 \end{gathered}[/tex]
So, the base is of length 7 units, that is, the length of the third side is 7 units.
