The area of the garden is 15*20 = 30 square meters;

so the area inside the fence is 2*300 = 600 square meters.

Thus this part is solved: it is easy part.


Now let start working on the second question.



Lex x be the uniform distance around the flower bed.


Then the dimensions of the fence are  (15+2x) meters width and (20+2x) meters length.


The area inside the fence is then  (15+2x)*(20+2x).


From here you have this equation to determine x


    (15+2x)*(20+2x) = 2*15*20 = 600.


Reduce this equation to the standard quadratic equation form and solve using the quadratic formula.


    4x^2 + 70x - 300 = 0.


It has no solution/solutions in integer or rational numbers, so other solution methods (guessing or factoring)
do not work.


When you find the value of x, you determine the perimeters as

    (15+2x) + (20+2x) + (15+2x) + 20+2x).