Question

The area of a small rectangular plot is $ 84 m^{2}$.If the difference between its length and the breadth is 5 m; find its perimeter.

Answer 1

 Hint: Here, we will be using the formula of perimeter and area of a rectangle.

Complete step-by-step answer:
Given:
The area of a small rectangular plot is$ 84 m^{2}$.
Let us take the length of the rectangular plot as l and breadth of the rectangular plot as b.
According to the question, the difference between its length
and the breadth is 5 m.
Therefore we get, l-b = 5m
Find l, l=b+5
Area of the rectangular plot is $ 84 m^{2}$
Using the formula of area of a rectangle, $ l \times b=84 m^{2}$
Substitute the value of l,
$ (b+5) \times b=84 m^{2}$
Simplify the equation,
$ (b+5) \times b=84 $
$ b^{2}+5b-84 =0$
Solve the quadratic equation,
$ b^{2}+12b-7b-84 =0$
$\Rightarrow b(b+12)-7(b+12)=0$
$\Rightarrow (b-7)(b+12)=0$


We get, b=7 and b=-12
But we know that a side can never be negative. Thus the solution b=-12 is rejected.
The breadth is 7 m
Find value of l,
l=7+5=12 m
Find the perimeter,
Perimeter=2(l+b)
                  =2(7+12)m
                  =2(19)m
                  =38 m

Note: To solve these types of problems first find the unknown values from the known values using the formulas.