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

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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) About Me  (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
a%5E2-b%5E2=55
"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 4a .
The perimeter of the smaller field (in m) is 4b , and twice the perimeter of the smaller field (in m) is 2%284b%29=8b .
So, "The perimeter of the larger field exceeds twice that of the smaller by 8 meters" translates into the equation
4a-8b=8 ,
which simplifies (dividing both sides of the equal sign by 4) into
a-2b=2 , so a=+2b%2B2 and a%5E2=4b%5E2%2B8b%2B4 .
Substituting 4b%5E2%2B8b%2B4 for a%5E2 in a%5E2-b%5E2=55 ,
we get
4b%5E2%2B8b%2B4-b%5E2=55 , which simplifies to 3b%5E2%2B8b-51=0
We can solve that by factorizing the polynomial at the left of the equal sign to get
%28b-3%29%283b%2B17%29=0 , whose positive solution highlight%28b=3%29 is the
only solution that makes sense.
Substituting 3 for b in a=+2b%2B2 , we find highlight%28a=8%29 .