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?

1 Answer
Jun 21, 2016

Answer:

#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#