SOLUTION: A rectangle has dimensions of (x + 2) and (3x + 3). Determine the exact value of x so that the perimeter and area of the rectangle will have the same numerical value.

Algebra ->  Rectangles -> SOLUTION: A rectangle has dimensions of (x + 2) and (3x + 3). Determine the exact value of x so that the perimeter and area of the rectangle will have the same numerical value.      Log On


   

Question 257193: A rectangle has dimensions of (x + 2) and (3x + 3). Determine the exact value of
x so that the perimeter and area of the rectangle will have the same numerical
value.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter of rectangle=2L+2W (L=Length, W=Width)=2(x+2)+2(3x+3)
Area of rectangle=L*W=(x+2)(3x+3)
So our equation to solve is:
(x+2)(3x+3)=2(x+2)+2(3x+3) get rid of parens
3x^2+3x+6x+6=2x+4+6x+6 simplify some
3x^2+9x+6=8x+10 subtract 8x and also 10 from each side
3x^2+9x+6-8x-10=8x+10-8x-10 collect like terms
3x^2+x-4=0 quadatic in standard for; solve using quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-1+%2B-+sqrt%28+1%5E2%2B4%2A3%2A4+%29%29%2F%282%2A3%29+
x+=+%28-1+%2B-+sqrt%28+49+%29%29%2F%286%29+
x+=+%28-1+%2B-+7+%29%2F%286%29+
x=(-1+7)/6=1-------------------------------ans
and
x=(-1-7)/6=-8/6------disregard, x cannot be negative
CK
Width=x+2=1+2=3
Length=3x+3=3+3=6
Perimeter=2*3+2*6=18
Area=3*6=18
Hope this helps--ptaylor