Question

The length of a rectangular board exceeds its breadth by $8cm$. If the length were decreased by a $4cm$ and the breadth doubled. the area of the board would be increased by $256sq.cm$,. Find the length of the board.

Answer 1

We have,

Let the length of rectangular board$=xcm.$

The breadth $=ycm.$

Now,

According to given question,

$length=breadth+8$

$x=y+8......\left(1\right)$

Again, according to given question,

$(x-4)2y=256$

$\Rightarrow (x-4)y=128$

$\Rightarrow xy-4y=128......\left(2\right)$

Put the value of x in equation ( 2) and we get,

$(y+8)y-4y=128$

$\Rightarrow y^2+8y-4y-128=0$

$\Rightarrow y^2+4y-128=0$

Using quadratic formula and we get,

$y=\frac{-4\pm \sqrt{16+4\times 1\times 128}}{2\times 1}$

$y=\frac{-4\pm \sqrt{16+512}}{2}$

$y=\frac{-4\pm \sqrt{528}}{2}$

$y=\frac{-4\pm \sqrt{528}}{2}$

$y=\frac{-4\pm 4\sqrt{33}}{2}$

$y=-2\pm 2\sqrt{33}$

$y=2(-1\pm \sqrt{33})$

Put the value in equation ( 1) and we get,

$x=2(-1\pm \sqrt{33})+8$

$x=-2\pm 2\sqrt{33}+8$

$x=6\pm 2\sqrt{33}$

Hence, this is the answer.