Q3 of 21 Page 67

Calculate the perimeter of the triangle shown below.


We know that sum of angles of a triangle is 180°.


⇒ ∠A + ∠B + ∠C = 180°


⇒ 30° + 105° + ∠C = 180°


⇒ ∠C = 180° - 135°


∴ ∠C = 45°


We know that the sine rule is = =.


In the triangle above, we have


⇒ c = 2 m;


a, b =?


Consider






∴ a = √2 ≈ 1.41 m


Now consider = ,


⇒ b






= √3 + 1


∴ b = √3 + 1 ≈ 1.73 + 1 = 2.73 m


We know that perimeter of a polygon is the sum of all its sides.


∴ Perimeter = a + b + c


= 1.41 + 2.73 + 2


= 6.14 m


More from this chapter

All 21 →
1

The hypotenuse of a right triangle is metres and another side is metre. Calculate its perimeter correct to a centimetre.

 2

The picture shows an equilateral triangle cut into halves by a line through vertex.


i) What is the perimeter of a part?


ii) How much less than the perimeter of the whole triangle is this?

 4

We have seen how we can draw a series of right triangles as in the picture.


i) What are the lengths of the sides of the tenth triangle?


ii) How much more is the perimeter of the tenth triangle than the perimeter of the ninth triangle?


iii) How do we write in algebra, the difference in perimeter of the nth triangle and that of the triangle just before it?

 5

What is the hypotenuse of the right triangle with perpendicular sides √2 centimetres and √3 centimetres? How much larger than the hypotenuse is the sum of the perpendicular side?