Question

Construct an equilateral triangle with sides 5 cm and justify the construction. Construct perpendicular bisectors of all sides and angle bisectors of all angles of the same triangle. Write the inference of your observation.​

Answer 1

ANSWER

Steps of construction:

1. Draw equilateral ΔABC according to the given measures.

2. Draw the perpendicular CD from C to AB.

Now CD is the height h=52−(25)2=253=4.3 cm of the triangle. Draw perpendicular bisector of CD to get DE = h/2.

Area of ΔABC=21×AB×h=AB×2h

To draw a square of area AB×(h/2), the side of the square should be AB×2h=25(3)41=3.3 cm.

Steps of construction:

1. Draw PQ=AB+2h=3.3 cm.

2. At the point Q and P, draw angles of 90˚ on the same side of PQ.

3. Cut those perpendicular lines at 3.3 cm at R and S.

4. Join RS.

5. Area of square PQ×QR=3.3×3.3 cm2≈10.89 cm2