Given:
The base of an isosceles triangle is 16 cm long.
The equal sides are each 22 cm long.
To find:
The height of the triangle.
Solution:
We know that the altitude of an isosceles triangle divides the base into two equal parts as shown in the below figure.
According to the Pythagoras theorem:
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Using Pythagoras theorem, we get
[tex]22^2=h^2+8^2[/tex]
[tex]484=h^2+64[/tex]
[tex]484-64=h^2[/tex]
[tex]420=h^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{420}=h[/tex] (Because side cannot be negative)
[tex]2\sqrt{105}=h[/tex]
Therefore, the height of the isosceles triangle is [tex]2\sqrt{105}[/tex] cm. Approximate height is 20.49 cm.
