A picture frame is 1o inches by 12 inches. The picture inside has an area of 63 square inches. The picture frame has a width of x inches. What is x?
2006-11-15 12:06:27 · 5 answers · asked by Julie J 1 in Science & Mathematics ➔ Mathematics
Then can you tell me how to solve it?
2006-11-15 12:20:27 · update #1
In other words 2 #'s that multiply together to get 57 but add together to get -22
2006-11-15 12:22:39 · update #2
Area of picture with frame is 120 inches. Area of picture is 63 inches.
x is width of frame, which is on each side of picture, so
(10-2x)(12-2x) = 63
120 - 44x + 4x^2 = 63
4x^2 - 44x + 57 = 0
Use quadratic formula to solve.
x = 19/2 (reject as too big) or
x = 3/2 or 1-1/2 inches.
Note: you have to use 2x because the frame goes around the whole picture, so it subtracts x from both sides.
2006-11-15 12:23:38 · answer #1 · answered by just♪wondering 7 · 0⤊ 0⤋
The picture dimensions are x less than the frame dimensions, so the picture size is 10-x by 12-x. The area of the picture is then (10-x)*(12-x) or 120 -22x + x^2. This must equal 63, giving the quadratic equation
x^2 - 22x +57 = 0
Solve this using quadratic formula or factoring, taking the positive root that makes sense; you get x=3. The other root (x=19) exceeds the frame dimensions, so it can't be right.
2006-11-15 20:13:48 · answer #2 · answered by gp4rts 7 · 0⤊ 0⤋
12
2006-11-15 20:16:22 · answer #3 · answered by Anonymous · 0⤊ 0⤋
your question seems to answer itself. First you say the dimensions of the frame are 10 in X 12 in. Then you say the width of the picture frame is x inches. If I believe all this, then x = 10. the area of the picture seems to have nothing to do with this.
Am I missing something?
2006-11-15 20:17:27 · answer #4 · answered by Marcella S 5 · 0⤊ 0⤋
Isn't the width 10 inches?
i don't know what's up with that, but you set up the problem like this: 63 squared = X times (whatever the height is)
2006-11-15 20:18:31 · answer #5 · answered by annie 2 · 0⤊ 0⤋