Question 118529
The key  in this one is "the area is INCREASED by 512 m2.
That means the area of the uniform strip is 512 m2.
If I call the width of the added strip {{{x}}},
Then going around the parking lot,
{{{512 = 40x +  x^2 + 16x + x^2 + 40x + x^2 + 16x + x^2}}}
{{{512 = 4x^2 + 80x + 32x}}}
{{{512 = 4x^2 + 112x}}}
subtract 512 from both sides
{{{4x^2 + 112x - 512 = 0}}}
{{{x^2 + 28x - 128 = 0}}}
solve by compleying the square
{{{x^2 + 28x = 128}}}
{{{x^2 + 28x + (28/2)^2 = 128 + (128/2)^2}}}
{{{x^2 + 28x + 196 = 128 + 196}}}
{{{(x + 14)^2 = 324}}}
{{{x + 14 = 18}}}
{{{x = 4}}} m answer
check answer
{{{512 = 4x^2 + 112x}}}
{{{512 = 4*16 + 112*4}}}
{{{512 = 64 + 448}}}
{{{512 = 512}}}
OK