Question

The perimeter of a rectangular field is 82m and its area is $400m^2.$ Find the breadth of the rectangle.

Answer 1

Let us take the length to be ‘$l$’ and the breadth to be ‘$b$'.

Now we now that perimeter of a rectangle = $2(l+b)=82$

$l+b=41$

$b=41-l$............let this be equation one.

Now, area of rectangle = \(l x b = 400\)

using equation one, substituting value of b

$l(41-l)=400$

$41l-l^2=400$

$l^2-41l+400=0$

Using splitting the middle term method,

$l-25l-16l+400=0$

$l(l-25)-16(l-25)=0$

$(l-25)(l-16)=0$

Thus

$l=25m$ or$l=16m$

Conventionally, we take length of a rectangle greater than the breadth. Thus,

$l=25m$

And, $b=41-l=41–25=16m$

Thus breadth of the rectangle is 16m.