If the length of a rectangle is (x+4) and the width of the rectangle is (x+1) and the area of the rectangle is 100, what does x equal?

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Answer 1 · 2016-06-21T05:18:19

$x=7.612$

Here, the length of a rectangle is $(x+4)$ and the width of the rectangle is $(x+1)$ and the area of the rectangle is $100$ .

Hence as area is product of length and width, we have

$(x+4)(x+1)=100$ or

$x^2+4x+x+4=100$ or

$x^2+5x-96=0$

as discriminant is $5^2-4*1*(-96)=25+384=409$ is not the square of a rational number, we will have to use quadratic formula and

$x=(-5+-sqrt409)/2=(-5+-20.224)/2$ i.e.

$x=7.612$ or $x=-12.612$

But as length cannot be negative, $x=7.612$