SOLUTION: The perimeter of a square garden is 12m greater than the perimeter of a smaller square garden. The area of the larger garden is 105 m squared greater than that of the smaller garde

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Question 31358This question is from textbook Algebra: Structure and Method Book 1
: The perimeter of a square garden is 12m greater than the perimeter of a smaller square garden. The area of the larger garden is 105 m squared greater than that of the smaller garden. Find the dimensions of the larger garden. This question is from textbook Algebra: Structure and Method Book 1

Found 2 solutions by Fermat, acerX:
Answer by Fermat(136) (Show Source):
You can put this solution on YOUR website!
Both gardens are square, therefore the sides of any one garden are all the same.
Let the sides of the large garden be a.
Let the sides of the small garden be b.
P1 = 4a (P1 is perimeter of large garden)
P2 = 4b (P2 is perimeter of small garden)
A1 = a� (A1 is area of large garden)
A2 = b� (A2 is area of small garden)
So,
P1 = P2 + 12 (The perimeter of a square garden is 12m greater than the perimeter of a smaller square garden.)
A1 = A2 + 105 (The area of the larger garden is 105 m squared greater than that of the smaller garden)
Using the 1st set of four eqns to substitute for A1,A2,P1,P2 into the 2nd set of two eqns, we get
4a = 4b + 12 ---------------(1)
a� = b� + 105 --------------(2)
from (1), a = b + 3
substitute for a = b + 3 into (2)
(b+3)� = b� + 105
b� + 6b + 9 = b� + 105
6b + 9 = 105
6b = 96
b = 16
======
a = 19
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Answer by acerX(62) (Show Source):
You can put this solution on YOUR website!
s=side of the small garden
s+12=side of the large garden
.
the equation would be:
.
FOIL the left side
subtract the
subtract the 144
divide by 24
length CANNOT be negative

.
side of the larger garden = s +12
OR