SOLUTION: The area of a square field exceeds that of another square by 55 square meters. The perimeter of the larger field exceeds twice that of the smaller by 8 meters. What are the sides o

Question 1184836: The area of a square field exceeds that of another square by 55 square meters. The perimeter of the larger field exceeds twice that of the smaller by 8 meters. What are the sides of the: (a) Larger Field (b) Smaller Field ?
Found 2 solutions by greenestamps, KMST:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let x be the side of the larger square and y be the side of the smaller square. Then

The area of the larger is 55 more than the area of the smaller:
x^2-y^2=55

The perimeter of the larger is 8 more than the perimeter of the smaller (so the side of the larger is 2 more than the side of the smaller):
x=y+2

With that pair of equations, you clearly want to use substitution.

(y+2)^2-y^2=55

That is easily solved for y; then x is y+2.

I leave it to you to finish the calculations.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
a=side length (in m) of the larger square field
b=side length (in m) of the smaller square field
The area of a square field exceeds that of another square by 55 square meters translates into the equation

"The perimeter of the larger field exceeds twice that of the smaller by 8 meters" requires carefully reading and thinking.
The perimeter of the larger field (in m) is .
The perimeter of the smaller field (in m) is , and twice the perimeter of the smaller field (in m) is .
So, "The perimeter of the larger field exceeds twice that of the smaller by 8 meters" translates into the equation
,
which simplifies (dividing both sides of the equal sign by 4) into
, so and .
Substituting for in ,
we get
, which simplifies to
We can solve that by factorizing the polynomial at the left of the equal sign to get
, whose positive solution is the
only solution that makes sense.
Substituting for in , we find .
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