Question

Construct a triangle $ABC$, whose perimeter is $12cm$ and whose sides are in the ratio $3:4:5$

Answer 1

Steps of construction

1. Draw a line segment and locate points $X,Y$ such that $XY=12cm$.

2. Draw a ray $XZ$, making an acute angle with $XY$ and drawn in the down-ward direction.

3. From $X$, locate $(3+4+5)=12$ points at equal distances along $XZ$.

4. Mark point $L,M,N$ on $XZ$ such that $XL=3$ parts, $LM=4$ parts and $MN=5$ parts.

5. Join $NY$. Through $L$ and $M$, draw $LB\parallel NY$ and $MC\parallel NY$, intersecting $XY$ in $B$ and $C$ respectively.

6. With $B$ as center and $BX$ as radius, draw an arc; with $C$ as a centre and $CY$ as radius, draw an arc cutting the previous arc at $A$.

7. Join $AB$ and $AC$.

Then $ABC$ is the required triangle.