Question

1) Find the missing side length.
х
12 in.
18 in.

Answer 1

x = 6
`√(5)`

Explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 12² = 18²

x² + 144 = 324 ( subtract 144 from both sides )

x² = 180 ( take the square root of both sides )

x =
`√(180)`

=
`√(36(5))`

=
`√(36)` ×
`√(5)`

= 6
`√(5)` ← exact value

Answer 2

The missing side length is 6√5.

The given information suggests the use of the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse c is equal to the sum of the squares of the other two sides a and b.

In this case, x is one of the legs, and 12 is the other leg, while 18 is the hypotenuse.

The Pythagorean theorem equation is:

`\[a^2 + b^2 = c^2\]`

In this context:

`\[x^2 + 12^2 = 18^2\]`

Now, solve for \(x\):

`\[x^2 + 144 = 324\]`

Subtract 144 from both sides:

`\[x^2 = 180\]`

Take the square root of both sides:

`\[x = √(180)\]`

Simplify:

`\[x = 6√(5)\]`

So, the missing side length x is 6√5 inches.