Question

Find the length of the third side. If necessary, write in simplest radical form. ​

Answer 1

Answer:

Length of third side of triangle is 10.

Step-by-step explanation:

Here we have,

Base = 6

hypotenuse = 2 √34

And it's a right angle triangle

Solution :-

Using Pythagoras theorem

(Perpendicular) ²+(Base) ²= (hypotenuse) ²

Let the missing side be x.

substitute the value into the theorem

( x ) ² + ( 6 ) ² = ( 2√34 ) ²

Multiplying the values

x² + 36 = 136

now, Solve it

x ² = 136- 36

x ² = 100

x = √ 100

x = 10

Hence , length of third side of triangle is 10.

Answer 2

Answer:

The length of the third side is equal to 10.

Step-by-step explanation:

In order to solve this, we need to know that in a right-angled triangle, the following is true:

$c = \sqrt{a^{2} + b^{2} }$   (where "c" is the hypotenuse and "a" and "b" are the legs of the right-angled triangle)

Now we can find the length of the missing side, lets say that the leg that we are trying to find is "a", then after plugging in the information we know, we get the following:

$c = \sqrt{a^{2} + b^{2} }\\2\sqrt{34} = \sqrt{a^{2} +6^{2} } \\\sqrt{136} = \sqrt{a^{2} + 36} \\136 = a^{2} + 36\\100 = a^{2} \\a = \sqrt{100} \\a = 10$

Therefore, the length of the third side is equal to 10.