SOLUTION: a rectangle is 6 cm long and 4 cm wide. If each dimension is increased by the same number of centimeters, a new rectangle is formed whose area is 39 square centimeters more than th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a rectangle is 6 cm long and 4 cm wide. If each dimension is increased by the same number of centimeters, a new rectangle is formed whose area is 39 square centimeters more than th      Log On


   

Question 391126: a rectangle is 6 cm long and 4 cm wide. If each dimension is increased by the same number of centimeters, a new rectangle is formed whose area is 39 square centimeters more than the area of the original rectangle. By how may centimeters was each dimension increased?
Answer by lwsshak3(11628) About Me  (Show Source):
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let x =number of cm each side of the rectangle was increased
area of rectangle = length * width
length of new rectangle = (x+6)cm
width of new rectangle = (x+4)cm
given area of new triangle =39 cm^2
(x+6)(x+4)=39
x^2+10x+24=39
x^2+10x-15=0
use the following quadratic formula to solve for x
with a =1,b=10,c=-15
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=((-10)ħsqrt(10^2-4*1*(-15))/2*1
= ((-10)ħsqrt(100+60)=-10ħsqrt(160))2

=(-10ħ12.65)/2=2.65/2 or -22.65/2
=1.33 or -11.33(reject)
ans: each side of the rectangle was increased by 1.33 cm
check: 7.33*5.33=39.07 (approximate because of rounding to two decimal places)