Question

Construct $ABC$, an isosceles triangle with $AB=AC=13$ cm and $BC=10$ cm. Calculate the length of perpendicular from $A$ to $BC$.

Answer 1

To construct a triangle with these three given sides,
1. First draw the base , say $BC=10cm$
2. Set the width of the compass as one side $AB=13cm$ and draw an arc from $B$ on any one side of the line segment $BC$
3. Similarly, set the width of the compass as the other side $AC=13cm$ and draw an arc from $C$ on the same side of the line segment $BC$ as done in Step 2
4. Mark the intersection of the two arcs as $A$
5. Join points $A;B$ and $A;C$ using a ruler.
6. $ABC$ is a required triangle.
To find the length of the perpendicular from $A$ to $BC$, join the mid point of $BC$ that is $D$ to $A$
On measuring $AD=12cm$