For triangle FGH, which of the following is an expression for y in terms of x?

Question

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.

Answer 1

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.