Question

Construct an isosceles triangle $ABC$ in which base $BC=6.5cm$ and altitude from A on $BC$ is $4cm$

Answer 1

Steps of construction:
(1) Draw a line segment $BC$ whose length is $6.5cm$
(2)Draw the perpendicular bisector of $BC$; call it $XY$ with $Y$ on $BC$
(3)With $X$ as centre and radius $4cm$, draw an arc cutting $XY$ at $A$; join $AB$ and $AC$.
Therefore $ABC$ is the required triangle.