Let the width of rectangle be x
then length according to question is (x+4)
Since diagonal of rectangle divides the rectangle into two right angled triangle
So according to Pythagorean theorem
Diagonal^2= Length^2 + Width^2 ---------- (1)
According to question, Diagonal = 10 m;
Therefore , putting the values in (1)
(10)^2=(x+4)^2+x^2
100 = x^2+8x+16+x^2
100 = 2x^2+8x+16
100-16 = 2x^2+8x
84=2x^2+8x
dividing both side by 2
42= x^2+4x
x^2+4x-42=0
by the help of quadratic formula
picture is attached below, from picture value of x=4.73 m
so x=width= 4.73m
(x+4) = length= (4.73+4)= 8.73m
Therefore the dimension of the garden is (8.73*4.73)meters.