Question

Construct a right triangle whose base is $12\mathrm{cm}$ and sum of its hypotenuse and other side is $18\mathrm{cm}$.

Answer 1

Let $∆\mathrm{ABC}$ be the right angled triangle where $\mathrm{BC}=12\mathrm{cm}$, $\angle \mathrm{B}=90°$ and $\mathrm{AC}+\mathrm{AB}=18\mathrm{cm}$

Steps for construction :

Step 1: Draw a line segment of base $\mathrm{BC}=12\mathrm{cm}$.

Step 2: Measure and draw $\angle \mathrm{B}=90°$ and draw the ray $\mathrm{BX}$.

Using a compass measure $18\mathrm{cm}$.

Step 3: Considering $\mathrm{B}$ as a centre and draw an arc on the ray $\mathrm{BX}$ which cut it at point $\mathrm{D}$. Join $\mathrm{DC}$.

Step 4: Now draw the perpendicular bisector of the line $\mathrm{DC}$

The intersection point on $\mathrm{BD}$ is taken as $\mathrm{A}$. Now join $\mathrm{AC}$.

Hence, $∆\mathrm{ABC}$ is the required triangle.