Question

Construct a triangle ABC, whose perimeter is 14 cm and sides given are in the ratio of 3 : 5 : 6.

Hint:

When constructing a triangle from three given side lengths, it is generally easiest to draw the longest side first as the base. This ensures that the other two arcs will intersect neatly above it.

Answer 1

Step 1: Calculation of Side Lengths
Before construction, we must determine the actual lengths of the three sides of the triangle.
Total Perimeter = 14 cm
Ratio of sides = 3 : 5 : 6
Sum of the parts of the ratio = 3 + 5 + 6 = 14
Now, calculate each side length:
Length of side 'a' = \( \left(\frac{3}{14}\right) \times 14 \) cm = 3 cm
Length of side 'b' = \( \left(\frac{5}{14}\right) \times 14 \) cm = 5 cm
Length of side 'c' = \( \left(\frac{6}{14}\right) \times 14 \) cm = 6 cm
The task is to construct a triangle with sides of 3 cm, 5 cm, and 6 cm.
Step 2: Steps of Construction
Draw the longest side as the base for stability. Use a ruler to draw a line segment BC of length 6 cm.
Set your compass to a radius equal to the second side length, 5 cm.
Place the compass point on B and draw an arc.
Now, set your compass to a radius equal to the third side length, 3 cm.
Place the compass point on C and draw another arc that intersects the first arc. Label the intersection point A.
Join points A to B and A to C with a ruler.
Triangle ABC is the required triangle with sides 5 cm, 6 cm, and 3 cm, and a total perimeter of 14 cm.