The length, breadth and height of a solid cuboidal box are in the ratio 7:5:3 and its total surface area is 11502cm
2
. Its breadth is:

Let the length (l), breadth (b), and height (h) of the cuboid be 7x, 5x, and 3x respectively.
The formula for the total surface area (TSA) of a cuboid is:

TSA=2(lb+bh+lh)
Given TSA=11502cm
2
:

2[(7x×5x)+(5x×3x)+(7x×3x)]=11502
2[35x
2
+15x
2
+21x
2
]=11502
2×71x
2
=11502
142x
2
=11502
x
2
=
142
11502
​
=81
x=
81

​
=9
The breadth of the box is 5x:

Breadth=5×9=45cm