Question 31358
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 = a² (A1 is area of large garden)
A2 = b² (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)
a² = b² + 105 --------------(2)
from (1), a = b + 3
substitute for a = b + 3 into (2)
(b+3)² = b² + 105
b² + 6b + 9 = b² + 105
6b + 9 = 105
6b = 96
b = 16
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a = 19
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