Question

The perimeter of a rectangular plot is 60 m and its area is 200 sq metres. Find the dimensions of the plot.

Answer 1

Given: Perimeter = 60 m, Area = 200 m².

Step-wise calculation:

1. Let length = L and breadth = W.

Perimeter: 2(L + W) = 60

⇒ L + W = 30

⇒ W = 30 – L

2. Area: L × W = 200

⇒ L(30 – L) = 200

3. Expand: 30L – L² = 200

⇒ L² – 30L + 200 = 0

4. Solve quadratic:

Discriminant D = 30² – 4 × 1 × 200 

= 900 – 800

= 100, `sqrt(D) = 10`

`L = (30 ± 10)/2` 

⇒ L = 20 or L = 10

5. Corresponding W = 30 – L

⇒ if L = 20 then W = 10; if L = 10 then W = 20

The dimensions are 20 m by 10 m (length and breadth, in either order).

Check: 2(20 + 10) = 60 and 20 × 10 = 200.