perimeter = 2(a +b), where a = length and b = width
p = 68
a+b = 34
so
a = 34-b
.
diagonal = c = 26 cm
.
Pythagorean Theorem teaches us that:
.
c^2 = a^2 + b^2
.
Substitute for a = 34-b and c = 26
.
26^2 = (34-b)^2 + b^2
,
Collect terms.
.
676 = (b^2 -68b + 1156) + b^2
.
2b^2 -68b + 480 = 0
.
b^2 -34b +240 = 0