Question

An isosceles triangle has its base of $20$ cm and each of its equal sides is $26$ cm long.
Calculate its height.

Answer 1

Consider an Isosceles triangle ABC, with $AB=AC=26cm.BC=20cm$

Draw a perpendicular AD on non- congruent side BC.

In an Isosceles triangle a perpendicular bisects the non congruent side.

Hence, $BD=\frac{1}{2}BC=\frac{1}{2}\left(20\right)=10cm$

In $△ABD$,

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

${26}^2=A{D}^2+{10}^2$

$676=A{D}^2+100$

$A{D}^2=576$

$AD=24cm$