The triangle has legs of 4 meters and x meters. The hypotenuse is of y meters.

I thought the answer was x+4, but the answer key says it is sq. rt.(x^2 + 16)

Can you please explain why I am wrong and why the answer key is correct.

Thanks so much.
asked Dec 29, 2016 in Geometry Answers by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

y^2=4^2+x^2. Take square roots of each side: y=√(16+x^2), which is the same as given.

You have assumed that the square of x+4 is x^2+16, or that the square root of x^2+16 is x+4. The square of x+4=x^2+8x+16. (x+4)^2=(x+4)(x+4)=x^2+4x+4x+16=x^2+8x+16. So, in your reasoning, 8x would be unaccounted for.

You can prove this for yourself by example: Put x=3: y^2=4^2+3^2=16+9=25 so y=5; but x+4 would be 7, according to your reasoning. 

answered Dec 29, 2016 by Rod Top Rated User (487,620 points)
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
79,851 questions
83,688 answers
66,614 users