Question

Construct a scalene triangle $ABC,$ given base $AB=3cm,$ base angle $={90}^o$ and sum of the lengths $BC+AC=9cm$.

Answer 1

Given base side as $AB=3cm$

Base angle $={90}^o=\frac{\angle B}{\angle C}$

Sum of lengths of other two sides, $BC+AC=9cm$

Steps:

1. Draw the base $AB$, make an angle $PAB$ equal to the given angle

2. Cut a line segment $AD$(equal to $BC$ and $AC$) on ray $PA$

3. Join $BD$. Draw a $\angle DBQ$ equal to $\angle ADB$

4. Let ray $BD$ intersect $AD$ at point $C$

Then, $△ABC$ is the required triangle

i.e, $BC=3.7cm;AC=5.3cm$

$\angle AC+BC=3.7+5.3=9cm$

$\angle CAB={45}^o$

$\angle ABC={80}^o$