Question

In an isosceles triangle $ABC,AB=AC=25cm$ and $BC=14$ cm The measure of an altitude from $A$ on BC in $cm$ is

• A. $20$
• B. $22$
• C. $18$
• D. $24$

Answer 1

The correct option is D $24$

In $△ABC$,

Let the altitude be AD or BC.

AC=25 cm

AB=25 cm

BC=14 cm

$\therefore$ DC$=\frac{1}{2}\times BC$

$=\frac{1}{2}\times 14=7cm$

By Pythagoras theorem,

$A{D}^2+C{D}^2=A{C}^2$

$\Rightarrow A{D}^2+7^2={25}^2$

$\Rightarrow A{D}^2=625-49=576$

$\Rightarrow AD=24cm$