Respuesta :

bekkarmahdi702

Answer:

Step-by-step explanation:

First let's find the value of x :

We khow that the area of this triangle is 400 and it is given by the product of the base and the height over 2

  • the base is x
  • the height is 2x
  • Let A be the area : A= (2x*x)/2 =2x²/2  =x²
  • so x²= 400 ⇒ x= 20≥ 0 because it's a distance

Let's find the hypotenuse :

The pythagorian theorem :

  • h²= x²+(2x)²
  • h²= x²+ 4x²
  • h²= 5x²
  • x=20⇒ h²= 5*(20)²
  • h²= 2000
  • h= 20[tex]\sqrt{5}[/tex] ≥0 because it is a distance

A) Given the area of a triangle is

B•h/2

B= x and H= 2x

Therefore 2x • x /2 = 400

2x^2 = 800

x^2 = 400

x = - or + 20

However since it’s the area it cannot be negative therefore the x value is 20

So the height is 40 (2x) while the base is 20 (x)

B) Given that the base is 20 and the height is 40, you can use Pythagoras Theorem where:

a^2 + b^2 = c^2

So 20^2 + 40^2 = 400 + 1600 = 2000

C^2 = 2000

C = square root 2000 ( insert in calculator and round up)

That gives you the hypotenuse.