Question

Construct a $\Delta PQR$ whose perimeter is $12$ c.m. and the lengths of whose sides are in the ratio of $2:3:4$.

Answer 1

Hint : To draw a triangle, we will draw a line of length of its perimeter. Then, we will draw a ray from one point in a straight line. After that, we will divide the ray into $9\left( 2+3+4 \right)$ equal parts and will mark the points length of 2, then 3 and after that 4. We will join the last point of the ray to the other end of the straight line. Then, we will draw parallel lines to the mark point that will cut the straight line in two points. Then, we will draw a circle of radius of one end to the first cut of straight length. After that, we will draw another circle of radius of length of second cut to the other end of straight length. Then we will join the intersection point of circles to the cut point of the straight line to draw the required triangle.


Complete step-by-step solution:
Since, we have given the ratio of sides as:
$\Rightarrow 2:3:7$
The perimeter of the triangle$=12$
Draw a straight line first named AB.

Then, draw a ray down the side of the straight line with an acute angle and divide it in some equal points. Then, we will draw the length of $2$ AC, then the length of 3 CDs and after that the length of 4 DM.

After that, we will join the line BM and draw the parallel line to BM at point C and point D that will intersect with the straight line.

Then, we will draw a circle from point P at the length of AP and another circle at point R at a length of RB.

Then, we will join the intersection point of both circles to the point P and pint R as:

Hence, the required circle will be drawn.

Note: Triangle is a $2D$ diagram made by using three sides. It has three points, angle and vertex also. There are total six types of triangles based on its sides and angle mentioned below:

Based on angle:	Based on sides:
Right angle Triangle	Equilateral Triangle
Acute Triangle	Isosceles Triangle
Obtuse Triangle	Scalene Triangle.