Explanation:

Correct option 1: 14 cm

Given:
The sum of the length, breadth, and height of a cuboid is 28 cm.
Total surface area of the cuboid is 588 cm²
Concept used:
In case of a cuboid,
Total surface area = 2 x (LB + BH + LH)
Diagonal = √(L² + B² + H²)
Where L = Length, B = Breadth, and H = Height
(A+B+C)²= A²+B² + C²+2x (AB+ BC+ CA)
Solution:
Let L, B, and H be the length, breadth, and height of the cuboid.
According to the question,
(L+B+H) = 28 ....(1)
2 x (LB + BH + LH) = 588 ....(2)
Diagonal = √(L² +B² + H²)
Now we know,
(L² + B² + H²) = (L+B+H)² - 2 x (LB + BH + LH)
=282-588
⇒784 - 588
=196
Hence, Diagonal = √(L² + B² + H²)=√196 = 14 cm