Question

Draw a right triangle in which the sides (other than hypotenuse) are of lengths $4cm$ and $3cm$. Then construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle.

Answer 1

Construct $△ABC$, the given right angled triangle, as follows:

Step 1: Draw base $BC$ of length $4cm$.

Step 2: Draw a right angle at point $B$.

Step 3: Draw an arc of radius $3cm$ on the right angle drawn from $B$ and label that point as $A$

Step 4: Join $A-C$.

$△ABC$ is the given triangle.

To construct $△EBD\sim △ABC$:

Step 1: Draw a ray $BX$ at an acute angle to line $BC$ on the opposite side of $A$.

Step 2: Mark $5$ equidistant points $B_1,B_2,B_3,B_4,B_5$ on ray $BX$.

Step 3: Join $B_3$ and $C$.

Step 4: Draw $B_{5}D$ parallel to $B_{3}C$ and label the intersection on the extension of $BC$ as $D$.

Step 5: Draw $DE$ parallel to $BA$ and label the intersection with the extension of $BA$ as $E$

$△EBD$ is the required triangle.