What is the value of x in a right triangle with a short leg measuring 5, a long leg measuring 5, and the hypotenuse as x?
A. 10
B. 5
C. [tex]2\sqrt{5}[/tex]
D. [tex]5\sqrt{2}[/tex]
Answer (3)
l oo k a t t h e p i c t u re P y t ha g or a s t h eore m x 2 = 5 2 + 5 2 x 2 = 25 + 25 x 2 = 25 ⋅ 2 x = 25 ⋅ 2 x = 25 ⋅ 2 x = 5 2 A n s w er : D
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
Using the Pythagorean theorem, we find that the hypotenuse x in a right triangle with legs measuring 5 units each is 5 2 . Thus, the answer is option D. This follows from calculating x 2 = 25 + 25 to yield x = 50 .
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