Question

Perimeter of a rectangular garden is $360$ m and its area is $8000{\text{m}}^2$. Find the length of the garden and also find its breadth. (The length is greater then the breadth)

Answer 1

Let Length $=a$m

breadth$=b$m

Perimeter$=2(a+b)=360$m

$2(a+b)=360\Rightarrow a+b=180-\left(i\right)$

and area $=8000m^2$

$ab=8000\Rightarrow b=\frac{8000}{a}$

Putting this in $\left(i\right)$

$a+\frac{8000}{a}=180\Rightarrow a^2-180a+8000=0a=\frac{180\pm \sqrt{32400-32000}}{2}=\frac{180\pm \sqrt{400}}{2}=\frac{180\pm 20}{2}a=\frac{180+20}{2},\frac{180-20}{2}a=\frac{200}{2},\frac{160}{2}=100,80\therefore a=100,80$