Question

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

Answer 1

Answer:

Option B.

Step-by-step 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.

$\sqrt{48}=x$

$4\sqrt{3}=x$

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

Therefore, the correct option is B.

Answer 2

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 =