Question

What is the value of x? A right triangle with a short leg measuring 5, a long leg measuring 5, and the hypotenuse as x.

A. 10

B. 5

C.
`2\sqrt5`

D.
`5\sqrt2`

Answer 1

The answer is d.
If you are solving for a missing leg of a triangle you want to use Pythagoras Theorm.
a² + b² = c²
a and b will be the legs you have been given and c is your hypotenuse (x).
5² + 5² = c²
25 + 25 = c²
50 = c²
since you are solving for c not c² you must take the √ of 50
√50 does not come out as an even number so you must try to think of two numbers that you can multiply and get 50 one should be a perfect square. In this case it is 25 and 2
√25 = 5
√2 does not come out even so we express our answer as 5√2

Answer 2

`look\ at\ the\ picture\\\\Pythagoras\ theorem\\\\x^2=5^2+5^2\\\\x^2=25+25\\\\x^2=25\cdot2\\\\x=√(25\cdot2)\\\\x=√(25)\cdot\sqrt2\\\\x=5\sqrt2\\\\Answer:D`