Question

26) An equilateral triangle has an altitude of 6 cm. What is the length of the sides?

Answer 1

18
`√(3)`

Explanation:

1. Find length of one side
2. Find area

altitude h=
`(√(3)*a )/(2)`, where a equals the length of one side

6=
`(√(3)*a )/(2)`

a=
`(2*6)/(√(3) )`

a=
`(2*√(3) *√(3) *3)/(√(3) )`

Area of a triangle=
`(1)/(2) *base *height`

base=a

a=
`\sqrt[6]{3}`

h=6

area=
`(1)/(2) *6*6√(3)`

=18
`√(3)`

Answer 2

Answer: the length of the sides is 6.93 cm

Explanation:

In an equilateral triangle, all the sides and angles are equal. The bisectors of each angle meet at the midpoint of the triangle. This means that 3 right angle triangles can be formed. Each of the right angle triangles having angle 60°, 30° and 90°. The altitude of the triangle is the opposite side while the length of each side, x of the equilateral triangle represents the hypotenuse of the right angle triangle.

To find x, we would apply the Sine trigonometric ratio

Sin θ = opposite side / hypotenuse

Sin 60 = 6/h

h = 6/Sin 60 = 6/0.8660

h = 6.93cm