Question

The perimeter of a rectangular plot of land is 114 metres and its area is 810 square metres.

1. Take the length of plot as x metres. Use the perimeter 114 m to write the value of the breadth in terms of x. 
2. Use the values of length, breadth and area to write an equation in x. 
3. Solve the equation to find the length and breadth of the plot.

Answer 1

i. Perimeter $$= 2(\text{length} + \text{breadth}) = 114\text{ m}$$. 

$$\text{length} + \text{breadth} = 57\text{ m}$$. 

Since length is $$x\text{ m}$$, breadth $$= (57 - x)\text{ metres}$$.

ii. Area $$= \text{length} \times \text{breadth} = 810\text{ m}^2$$:

$$x(57 - x) = 810$$

$$57x - x^2 = 810$$

$$x^2 - 57x + 810 = 0$$ 

iii. Factoring: $$x^2 - 30x - 27x + 810 = 0$$

$$x(x - 30) - 27(x - 30) = 0$$

$$(x - 30)(x - 27) = 0$$

$$x = 30 \quad \text{or} \quad x = 27$$

Taking length as the larger dimension, length $$= 30\text{ m}$$ and breadth $$= 57 - 30 = 27\text{ m}$$.