if area is 47.5cm squared and length is 3cm longer than width, what is length and what is width?

Question

If a rectangle is 3cm longer than it's width and it's area is 47.5cm squared what is it's length and it's width, and how do you find them?

Answer 1

Let rectangle width(b) = xcm

Then length(l) wouldbe x+3cm.

A = l*b

47.5 = x(x+3)

47.5 = x^2+3x

Subtract 47.5 from each side.

x^2+3x-47.5 = 0

Compre it to quadratic equation ax^2+bx+c = 0

a = 1,b = 3, c = -47.5

x = [-b±√(b^2-4ac)]/2a

x = [-3±√(9+190)]/2

x = [-3±√199]/2

x = [-3±14.10]/2

x = (-3+14.10)/2 and x = (-3-14.10)/2

x = 11.10/2 and x = -17.10/2

x = 5.55 and x = -8.55

Rectangle has positive dimension.

So x = b = 5.55cm

3+x = l = 8.55cm