Question

Find the value of X in the triangle shown below

Answer 1

Answer:

Choice A (x=5)

Step-by-step 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

$\sqrt{c^{2} } =\sqrt{25}$

$c =5$

Choice A (x = 5) is your answer

Answer 2

Answer:

A. x=5

Step-by-step 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.

$\sqrt{25}=\sqrt{x^2}$

$\sqrt{25}=x$

$5=x$

Therefore the correct answer is A: x=5