Q1 of 21 Page 75

Calculate the length of the sides of the equilateral triangle on the right, correct to a millimetre.

The figure is attached below:



An equilateral triangle has all sides of equal length,


i.e.,


AB = BC = AC


AD is perpendicular to BC,


∴ D is the midpoint of BC


⇒ BD = DC = 1/2 BC = 1/2 AB =1/2 AC


Now using Pythagoras theorem,


AD2 + BD2 = AB2


⇒ 42 + (1/2 AB)2 = AB2


⇒ AB2 + 1/4 AB2 = 42







Hence, sides of triangle are 3.6 cm


More from this chapter

All 21 →
4

All red triangles in the picture are equilateral. What is the ratio of the sides of the outer and inner squares?


 5

From the pair of numbers given below, pick out those whose product is a natural number or a fraction:

(i) √3, √12


(ii) √3, √1.2


(iii) √5, √8


(iv) √0.5, √8


(v) ,


2

The picture shows the vertices of a regular hexagon connected by lines.


i) Prove that the inner red hexagon is also regular.


ii) How much of a side of the large hexagon is a side of the small hexagon?


iii) How much of the area of the large hexagon is the area of the small hexagon?

 3

Prove that Use this to compute correct to two decimal places.