Question

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?

Answer 1

`x=7.612`

Explanation:

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`