Question 534076: Sum of the ares of 2 square is 468 msquare. If the difference of their perimeter is 24m. Find the sides of 2 square. Found 2 solutions by Alan3354, fcabanski:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Sum of the areas of 2 squares is 468 m squared. If the difference of their perimeters is 24m, find the sides of the 2 squares.
------------------- Areas
4s1 - 4s2 = 24 Perimeters, s1 is larger
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s1 - s2 = 6
s1 = s2 + 6
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(s - 12)*(s + 18) = 0
Sides are 12 & 18 meters
You can put this solution on YOUR website! Call S = sides of square 1 (square S). We'll make this one the square with the larger perimeter.
Call T = sides of square 2 (square T)
The perimeter of square 1 is S + S + S + S = 4S. The area of square 1 is S^2
The perimeter of square 2 is T + T + T + T = 4T. The area of square 2 is T^2
We called S the square with the larger perimeter, and we know the difference is 24, so:
4S = 4T + 24
We know the sum of their areas is 468.
S^2 + T^2 = 468
Two equations, two unknowns. So let's solve the first equation for S in terms of T.
4S = 4T + 24 divide both sides by 4 ---> S = 4T/4 + 24 = T+6
Substitute that for S in the area equation, so we can solve it for T.
S^2 + T^2 = 468 (substitute T+6 for S)
(T+6)^2 + T^2 = 468 Use FOIL to square T+6
T^2 + 12T + 36 +T^2 = 468 Combine the T^2 terms, subtract 468 from each side.
2T^2 + 12T - 432 = 0
Factor 2 from each term.
T^2 + 6T - 216 = 0 Factor using reverse FOIL.
(T+18)(T-12) solve each for T
T+18=0 (subtract 18 from each side) T=-18 This solution is valid, but not in the real world because the side of a square can't be a negative number.
T-12=0 (add 12 to both sides) T = 12
Sides of T = 12. It's perimeter is 4*12 = 48m
Remember earlier we found that S = T+6 = 12 + 6 = 18. Thus the perimeter of S is 4*18 = 72m
Now check if these are the correct answers.
The perimeter of S should be 24m more than the perimeter of T.
72-48 = 24 CHECK
The combined areas should be 468 m^2.
12^2 + 18^2 = 144+324 = 468 CHECK
HURRAH...we found the answer.
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