Question

What is the approximate value of x in this figure?
19 POINTS

Answer 1

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

`√(13)` = c

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

a = 3

b =
`√(13)`

c = x

let's plug our values into the Pythagorean theorem.

3^2 + (
`√(13)`)^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

`√(22)` = x

But the problem is asking for the approximate value, the approximate value of
`√(22)` = 4.69 in

Answer 2

4.69 inches (2 decimal places)

Explanation:

Refer to image attached to this answer:

Using Pythagoras Theorem:

`AB^2+AC^2=BC^2`

`2^2+3^2=BC^2`

`4+9=BC^2`

`BC^2=13`

-------------------------

Using Pythagoras Theorem,

`BC^2+CD^2=BD^2\ (x)`

`13+3^2=BD^2`

`13+9=BD^2`

`BD=√(22) = 4.69\ (2d.p.)`