Question

Find the value of X in the triangle shown below

Answer 1

A. x=5

Explanation:

This triangle is a right triangle. We know this because of the little square in the corner that represents a right angle. Therefore, we can use Pythagorean Theorem.

`a^2+b^2=c^2`

where a and b are the legs and c is the hypotenuse.

We know that 4 and 3 are the legs, because they form the right angle. We also know that x is the hypotenuse, because it is opposite the right angle.

a=4

b=3

c=x

Substitute these values into the formula.

`4^2+3^2=x^2`

Evaluate the exponents.

4^2 is the same as 4*4, which is 16.

3^2 is the same as 3*3, which is 9.

`16+9=x^2`

Add 16 and 9.

`25=x^2`

We are trying to find x, which means we have to get x alone. x is currently being squared. To undo this, take the square root of both sides. The exponent and square root will cancel, leaving x by itself.

`√(25)=√(x^2)`

`√(25)=x`

`5=x`

Therefore the correct answer is A: x=5

Answer 2

Choice A (x=5)

Explanation:

You can get you answer either by using the 3-4-5 Triangle Rule or the Pythagorean theorem (
`a^(2) +b^(2) =c^(2)`)

Using the Pythagorean theorem:

Begin by plugging in 4 into a and 3 into b

`4^(2) +3^(2) =c^(2)`

`16 +9 =c^(2)`

`c^(2)= 25`

Then, find the square root of each side

`\sqrt{c^(2) } =√(25)`

`c =5`

Choice A (x = 5) is your answer