SOLUTION: An 8-inch-square picture is to be enlarged so it covers an area of 100 inches.How much longer will each side of the enlarged picture be?

Question 11406: An 8-inch-square picture is to be enlarged so it covers an area of 100 inches.How much longer will each side of the enlarged picture be?
Found 2 solutions by tishy, prince_abubu:
Answer by tishy(4) (Show Source): You can put this solution on YOUR website!
An 8-inch-square picture is to be enlarged so it covers an area of 100 inches.How much longer will each side of the enlarged picture be?
therefore 8x 4(no. of sides) = 32
so of 32 inches is taken up already then you ,msut see how much more is left there fore
100-32= 68
to see how much each side is enlarged by divide 68 into 4
you get an answer of 17
so if u add the 17 to the original 8 u get 25inches for each side and
25x4 = 100
answer!!! :-)
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
When you say 8-inch-square picture, I take it that you mean a picture with the dimensions 8 in by 8 in. If so, the area of that current picture is 64 square inches. I think you're asking for how many inches will have to be added to each side of that square picture so that the area will be enlarged to 100 square inches.

<------- You know that a picture with sides that are 8 inches long has an area of 64 square inches.

<----- You wonder how much to add (+x) to the length and width of the picture so that the resulting area will be 100 square inches.

<------ FOILed

<------ Re-ordered the terms on the left side because it looks better this way.

<------ Subtract 100 from both sides. This way, the right side will be zero. We can only solve quadratic equations if the right side is equal to zero!

<-------- This is reverse-FOILING, or factoring. What we did was found two integers that when times'd together gives us -36 BUT add up to +16. 18 and -2 do it, so we put it in (x +/- ?)(x +/- ? ) form.

From the above, we can tell that x = -18 or x = 2. Since -18 is NOT a valid value for a measure (because we can't have negative measurements), the 2 is the correct answer. So, if we add 2 to the sides of the 8 x 8 square, we'll end up with a 10 x 10 square, which indeed will have an area of 100 square inches.
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