Question

The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle?

5 StartRoot 2 EndRoot units
4 StartRoot 3 EndRoot units
10 StartRoot 2 EndRoot units
16 StartRoot 5 EndRoot units

Answer 1

Answer:The perimeter of parallelogram PQRS = 2\sqrt{10}+8\sqrt{2} ⇒

2nd answer

Step-by-step explanation:* Lets revise some properties of the parallelogram

- Each two opposite sides are parallel

- Each two opposite sides are equal

- Its perimeter is the twice the sum of two adjacent sides

* Lets solve the problem

∵ PQRS is a parallelogram

∵ The length of side SR is

∵ The length of side QR is

∵ SR and RQ are two adjacent sides

∵ The perimeter of parallelogram PQRS = 2(RQ + SR)

∴ The perimeter of parallelogram PQRS =

∵ =

∵ =

∴ The perimeter of parallelogram PQRS =

Answer 2

Option B.

Explanation:

It is given that the sides of an equilateral triangle are 8 units long.

Draw an altitude of the triangle.

Altitude of an equilateral triangle is perpendicular bisector.

Let x be the length of the altitude of the triangle.

According to the Pythagoras theorem

`hypotenuse^2=base^2+perpendicular^2`

Using Pythagoras theorem we get

`8^2=4^2+x^2`

`64=16+x^2`

`64-16=x^2`

`48=x^2`

Taking square root on both sides.

`√(48)=x`

`4√(3)=x`

The length of the altitude of the triangle is 4√3 units.

Therefore, the correct option is B.