Question 426919: a rectangular painting has the dimensions x and x+10. the painting is in a frame 2 inches wide. the total area of the picture and the frame is 936 in. what are the total dimensions of the painting
this is my problme solving question and my formula for solving ( factoring ) was ( x+2) (x+12)=936 i multiplied out and got x²+14x+24=936. i just don't understand where to go after i use completing the square and getting x=-38 and x=29 how do i find the dimensions from two x values
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! Your approach is right. But the area of the rectangle is actually (X+4)(X+14)=936 because you have to add 2 inches to each side to form a 2-inch border. Thus we have:
(X+4)(X+10+4)=936
(X+4)(X+14)=936
X^2 + 18X + 56 = 936
X^2 + 18X - 880 = 0
(X+40)(X-22) = 0
X = -40 or 22
We reject the negative answer, and we're left with X = 22. If we check this we get (22+4)(22+14)= 936, 26*36 = 936, 936 = 936.
Edited 3-13-2017
x * x+10=936
x²+10x-936=0
(x+36)(x-26)=0
x=-36 or 26
x+10=36
The dimensions of the entire picture and frame is 36" x 26". The dimensions of the picture itself is (36-4)x(26-4), or 32" by 22". ☺☺☺☺
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