Diagonal brace. The width of a rectangular gate is 2 meters

Question

(m) larger than its height. The diagonal brace measures square root of 6. Find the width and height.

Answer 1

It's not going to be a very tall gate.

Let x=height of the gate.
Then x+2 = width of the gate.

Using pythagoras theorem,
x^sup2;+(x+2)² = 6
2x² + 4x - 2 = 0
Solve for x to get:
x=±√2 -1
x=0.41421 or -2.41421 (approx.)
The second root is rejected (height cannot be negative).

Therefore the height is approximately 0.41 m and the width is approx. 2.41 m.

Answer 2

So just to be clear, I wanted to make sure...the 6 is inside a square root box/sign..does this change ? Thx.