Question

Helppp! find the missing triangle side length below using pythagorean theorem. leave answer in simplified radical form please!​

Answer 1

The side a measures $\sqrt{53}$ units and the side x measures $2\sqrt{7}$ units.

Step-by-step explanation:

Step 1:

According to the Pythagorean theorem, the square of the hypotenuse will be equal to the sum of the squares of the other two sides.

We use the triangle with sides 7 and 2 as we do not know the length of side x in the first triangle

In the given triangle, the hypotenuse is the side that is represented by a. The other sides on the triangle measure 7 and 2 units.

Step 2:

So according to the Pythagorean theorem,

$a^{2} =7^{2} +2^{2} = 49 + 4 =53.$

$a^{2} = 53, a = \sqrt{53} .$

Step 3:

Now for the first triangle, the same Pythagorean theorem can be used.

The length of the hypotenuse is $\sqrt{53}$ and the sides of the triangle are 5 and x.

So $\sqrt{53} ^{2} = 5^{2} + x^{2} , 53 = 25 + x^{2}.$

$x^{2} = 53 -25 = 28, x = \sqrt{28}.$

28 can be written as 7 times 4 and the root of 4 is 2 so $\sqrt{28} = \sqrt{4(7)} = 2\sqrt{7}$.

The length of x is $2\sqrt{7} .$