Question

Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure 2004-04-01-02-00_files/i0350000.jpgand 2004-04-01-02-00_files/i0350001.jpg.

A.
2004-04-01-02-00_files/i0350002.jpg
B.
2004-04-01-02-00_files/i0350003.jpg
C.
2004-04-01-02-00_files/i0350004.jpg
D.
2004-04-01-02-00_files/i0350005.jpg

Answer 1

Corrected Question:
Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure 2x\(^2\)-y\(^2\) and 2xy.

Answer 2

Okay use pythagoreans theorem

Do you know what that equation is?

Answer 3

Welp you left

Pythagorean Theorem
a\(^2\)+b\(^2\)=c\(^2\)

a and b are the legs, so we just substitute that into the equation

(2x\(^2\)-y\(^2\))\(^2\)+(2xy)\(^2\)=c\(^2\)

First simplify the legs (a and b)
=\((2x^2-y^2)^2\) \(=4x^4-4x^2y^2+y^4\)
=\((2xy)^2\) \(=4x^2y^2\)

So we now have

\((4x^4-4x^2y^2+y^4)+4x^2y^2\)

Combine like terms

\(4x^4\color{red}{-4x^2y^2}+y^4\color{red}{+4x^2y^2}\)
=\(4x^4+y^4\)

So we have

\(4x^4+y^4=c^2\)

Now we take the square root on both sides

\(c=\sqrt{4x^4+y^4}\)

Which happens to be A