Question

construct an equilateral triangle with sides 5cm and justify the construction ,construct perpendicular bisectors of all sides and angle 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=  $\sqrt{5^{2}-(\frac{5}{2} ^{2}) } = \frac{\sqrt[5]{3}}{2}= 4.3 cm$ of the triangle. Draw perpendicular bisector of CD to get DE = h/2.

Area of ΔABC=  $\frac{1}{2}$ ×AB×h=AB×  $\frac{h}{2}$

To draw a square of area AB×(h/2), the side of the square should be $\sqrt{AB*\frac{h}{2} } =\frac{5(3)^{\frac{1}{4} } }2{} } }$  =3.3 cm.