Question

A plot of land doubles in size by adding x meters to the length and x meters to width of land.if the original plot had an area of 200 by 300 meters, what is the value of x?

Answer 1

The original plot of land had dimensions (200 m)(300 m) = 60000 m^2, which is the product of L and W.

Twice that area would be 2(60000 m^2) = 120000 m^2 = (L+x)(W+x).  Expanding this, we get LW + Lx + Wx + x^2 = 120000 m^2.  Treat L and W as constants and x as the variable:

x^2 + (L+W)x + LW -120000 = 0 and LW=60000 (from above).

Substituting, 

x^2 + (L+W)x + 60000 - 120000 = 0, or x^2 + (L+W)x - 600000 = 0.  Unfortunately, we don't know the value of L+W  (unless we assume that L = 300 m and W = 200 m).  We could use the quadratic formula to solve the above equation for x in terms of (L+W).

I note that you wrote, "If the original plot had an area of 200 by 300 m^2 .... "

This is inappropriate and should read "If the original plot of land had DIMENSIONS 200 m by 300 m ...   

Ensure that you have copied down the original problem exactly as it was presented to you.