The breadth of a rectangular hall is 5/8 of its length. If the area of the…

Concept:

For a rectangle, Area = Length x Breadth. When the breadth is given as a fixed fraction of the length (B = k x L for some constant k), substituting into the area formula gives a single-variable equation in L: Area = k x L2, which can be solved for L, then for B, then for any combination of the two such as their difference.

Applying it here:

1. Let the length of the hall be L. Since the breadth is 5/8 of the length, B = (5/8)L.

2. Using Area = Length x Breadth: 160 = L x (5/8)L = (5/8)L2.

3. Rearranging gives L2 = 160 x (8/5) = 256, so L = 16 metres.

4. Finding the breadth: B = (5/8) x 16 = 10 metres.

5. Computing the difference: L - B = 16 - 10 = 6 metres.

Cross-check:

With L = 16 m and B = 10 m: the ratio B/L = 10/16 = 5/8 matches the given breadth-to-length ratio, and the area L x B = 16 x 10 = 160 square metres matches the given floor area, so both conditions in the problem are satisfied.

Result:

The difference between the length and the breadth of the hall is 6 metres.