Question

A marginal walk all round the inside of a rectangular field 30 m long and 28 m wide costs ₹ 56.00 at 50 paise per m² to construct it. Find the width of the walk.

Answer 1

Given: A rectangular field 30 m by 28 m has a marginal walk of uniform width x m all round the inside. The walk costs ₹ 56.00 at 50 paise per m².

Step-wise calculation:

1. Cost per m² = 50 paise = ₹ 0.50.

Area of walk

= `"Total cost"/"Rate"` 

= `56/0.5`

= 112 m²

2. Area of whole field

= 30 × 28

= 840 m²

Area of inner (remaining) rectangle

= 840 – 112

= 728 m²

3. If the walk width is x, inner rectangle dimensions = (30 – 2x) and (28 – 2x).

So, (30 – 2x)(28 – 2x) = 728.

4. Expand and simplify:

840 – 116x + 4x² = 728

⇒ 4x² – 116x + 112 = 0

⇒ Divide by 4: x² – 29x + 28 = 0

5. Solve quadratic:

Discriminant = 29² – 4 × 1 × 28 

= 841 − 112 

= 729 = 27²

`x = (29 ± 27)/2`

⇒ x = 28 or x = 1

6. x = 28 m is not feasible (exceeds half the smaller side), so choose x = 1 m.

The width of the walk is 1 metre.