SOLUTION: i have a story problem i am trying to figure out. I think the equation is going to be a^2+b^2=c^2 but im not quite sure the problem reads: The length of each side of a square is 3

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Question 649483: i have a story problem i am trying to figure out. I think the equation is going to be a^2+b^2=c^2 but im not quite sure the problem reads:
The length of each side of a square is 3 inches more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in2. Find the lengths of the sides of the two squares. (define the variable, write an equation, solve and label)
so far i have x^2+(x+6)^2=149 then i factored it out and came to 2x^2+12x-113=0 and from there im not sure what to do can you help.
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

i have a story problem i am trying to figure out. I think the equation is going to be a^2+b^2=c^2 but im not quite sure the problem reads:
The length of each side of a square is 3 inches more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in2. Find the lengths of the sides of the two squares. (define the variable, write an equation, solve and label)
so far i have x^2+(x+6)^2=149 then i factored it out and came to 2x^2+12x-113=0 and from there im not sure what to do can you help.

(x + 6)? Where did this come from?

Let length of one side of smaller square be S
Then one side of larger square = S + 3
Areas of smaller and larger squares = S%5E2 and %28S+%2B+3%29%5E2, respectively
Since their areas sum to 149 sq in., then: S%5E2+%2B+%28S+%2B+3%29%5E2+=+149
S%5E2+%2B+S%5E2+%2B+6S+%2B+9+=+149
2S%5E2+%2B+6S+-+140+=+0
2%28S%5E2+%2B+3S+-+70%29+=+2%280%29
S%5E2+%2B+3S+-+70+=+0

(S - 7)(S + 10) = 0

S – 7 = 0 OR S = - 10 (ignore)
S, or length of one side of smaller square = highlight_green%287%29 inches
Length of one side of larger square = 7 + 3, or highlight_green%2810%29 inches

I'll leave the check up to you!

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