Question 124363
The diagonal of the stage(10m) represents the hypotenuse of a right triangle whose legs are the width (W) and the length (L) of the rectangle.
But the problem states that the length (L) is 2 meters longer than the width (W), so the length can be expressed as: 
L = W+2.
Now we can apply the Pythagorean theorem ({{{c^2=a^2+b^2}}}) to solve this problem since we are dealing with a right triangle.
c is the hypotenuse of the right triangle, or the diagonal of the rectangular stage which is given as 10m.
a and b are the width of the stage (W) and the length of the stage (L = W+2).
Make the appropriate substitutions into the Pythagorean formula to get:
{{{10^2 = L^2+W^2}}} Substitute L = W+2
{{{100 = (W+2)^2+W^2}}}
{{{100 =  (W^2+4W+4)+W^2}}}
{{{100 = 2W^2+4W+4}}} Divide through by 2 to simplify a bit.
{{{50 = W^2+2W+2}}} Subtract 50 from both sides.
{{{W^2+2W-48 = 0}}} Solve this quadratic equation by factoring.
{{{(W-6)(W+8) = 0}}} Apply the zero product principle.
{{{W-6 = 0}}} or {{{W+8 = 0}}}
If {{{W-6 = 0}}} then {{{W = 6}}}
If {{{W+8 = 0}}} then {{{W = -8}}} Discard this solution as the width, W, must be a positive value.
{{{W = 6}}}
The width is 6 meters.
{{{L = W+2}}}
{{{L = 8}}}
The length is 8 meters.
Check:
{{{c^2 = a^2+b^2}}} Substitute c = 10, a = 8, and b = 6.
{{{10^2 = 8^2+6^2}}}
{{{100 = 64+36}}}
{{{100 = 100}}} OK!