Respuesta :

Estellia

Answer:

4.69 inches (2 decimal places)

Step-by-step explanation:

Refer to image attached to this answer:

Using Pythagoras Theorem:

[tex]AB^2+AC^2=BC^2[/tex]

[tex]2^2+3^2=BC^2[/tex]

[tex]4+9=BC^2[/tex]

[tex]BC^2=13[/tex]

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Using Pythagoras Theorem,

[tex]BC^2+CD^2=BD^2\ (x)[/tex]

[tex]13+3^2=BD^2[/tex]

[tex]13+9=BD^2[/tex]

[tex]BD=\sqrt{22} = 4.69\ (2d.p.)[/tex]

Ver imagen Estellia
Cytokine

First, we have to find the last remaining side of the leftmost triangle.

We can use the Pythagorean theorem.

The Pythagorean theorem: a^2 + b^2 = c^2

a = one leg

b = the second leg

c = the hypotenuse

In this problem,

a = 3

b = 2

c = ?

Let's plug our numbers into the Pythagorean theorem.

3^2 + 2^2 = c^2

Simplify the left side

9 + 4 = c^2

Add together like terms

13 = c^2

Take the square root of both sides

[tex]\sqrt{13}[/tex] = c

Now we can use the Pythagorean theorem on the rightmost triangle to find x.

a = 3

b = [tex]\sqrt{13}[/tex]

c = x

let's plug our values into the Pythagorean theorem.

3^2 + ([tex]\sqrt{13}[/tex])^2 = (x)^2

Simplify the left side

9 + 13 = x^2

Add together like terms

22 = x^2

Take the square root of both sides

[tex]\sqrt{22}[/tex] = x

But the problem is asking for the approximate value, the approximate value of [tex]\sqrt{22}[/tex] = 4.69 in

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