SOLUTION: a rectangular page in a book is to have an 18 cm by 23 cm illustration in the center with equal margins on all four sides. How wide should the margins be if the page has an area of

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a rectangular page in a book is to have an 18 cm by 23 cm illustration in the center with equal margins on all four sides. How wide should the margins be if the page has an area of      Log On


   

Question 169268: a rectangular page in a book is to have an 18 cm by 23 cm illustration in the center with equal margins on all four sides. How wide should the margins be if the page has an area of 594 square cm?
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
18*23=414 cm^2 is the center illustration.
(13+2x)(23+2x)=594
299+46x+26x+4x^2=594
4x^2+72x+299-594=0
4x^2+72-295=0
Using the quadratic equation x=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29 we get:
x=(-72+-sqrt[72^2-4*4*-295])/2*4
x=(-72+-sqrt[5184+4720])/8
x=)-71+-sqrt9904)/8
x=(-72+-99.5188)/8
x=27.5188/8
x=3.43986 cm. ans for the margin.
Proof:
(13+2*3.43986)(23+2*4.43986)=594
(13+6.8797)(23+6.8797)=594
19.8797*29.8797=594
594~594