SOLUTION: Can I please get some help to solve the following Quadratic Equation and show full working. I would really appreciate it. The length of a poster is 10cm longer than its width. I

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can I please get some help to solve the following Quadratic Equation and show full working. I would really appreciate it. The length of a poster is 10cm longer than its width. I      Log On


   

Question 811149: Can I please get some help to solve the following Quadratic Equation and show full working. I would really appreciate it.
The length of a poster is 10cm longer than its width. If the area of the poster is 1200cm2, what is the width of the poster?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let's the length of a poster be a and the width b
the area is A=a%2Ab.......eq.1
if the length is 10cm longer than its width, then
a=b%2B10cm.........eq.2
If the area of the poster is A=1200cm%5E2, then from eq.1
a%2Ab=1200cm%5E2......substitute a from eq.2
%28b%2B10cm%29%2Ab=1200cm%5E2.....solve for bto find the width of the poster
b%5E2%2B10b%2Acm=1200cm%5E2
b%5E2%2B10b%2Acm-1200cm%5E2=0....use quadratic formula

b+=+%28-10cm+%2B-+sqrt%28%2810cm%29%5E2-4%2A1%2A%28-1200cm%5E2%29+%29%29%2F%282%2A1%29+
b+=+%28-10cm+%2B-+sqrt%28100cm%5E2%2B4800cm%5E2+%29%29%2F2+
b+=+%28-10cm+%2B-+sqrt%28+4900cm%5E2+%29%29%2F2+
b+=+%28-10cm+%2B-+70cm+%29%2F2+....we need only positive solution because the width cannot be negative
b+=+%28-10cm+%2B+70cm+%29%2F2+
b+=+60cm+%2F2+
highlight%28b+=+30cm%29....the width of the poster
highlight%28a=40cm%29........the length of the poster