Question

The perimeter of a rectangle is $104m$. and its area $640m^2$. Find its length and breadth.

Answer 1

We have,

Perimeter of rectangle$=104m$

Area of rectangle$=640m^2$

Let the length of rectangle$=x$

And breadth$=y$

So,

According to given question,

$2(x+y)=104$

$\Rightarrow x+y=52......\left(1\right)$

Now,

$Area=640$

$x\times y=640$

$y=\frac{640}{x}......\left(2\right)$

From equation ( 1) and ( 2) to, and we get,

$x+y=52$

$\Rightarrow x+\frac{640}{x}=52$

$\Rightarrow x^2+640=52x$

$\Rightarrow x^2-52x+640=0$

$\Rightarrow x^2-(32+20)x+640=0$

$\Rightarrow x^2-32x-20x+640=0$

$\Rightarrow x(x-32)-20(x-32)=0$

$\Rightarrow (x-32)(x-20)=0$

If

$x-32=0$

$x=32$

If

$x-20=0$

$\Rightarrow x=20m.$

Put $x=32$

$y=\frac{640}{32}=20$

$y=20m.$

Hence, this is the answer.