Two gardens

The flower garden has a square shape. The new garden has a rectangular shape; one dimension is 8 m smaller, and the other is twice as large as in a square garden. What were the original and new garden dimensions if both gardens' areas were the same?

Correct answer:

a =  16 m
x =  8 m
y =  32 m

Step-by-step explanation:

S1=S2 S1=a2 S2= x y x = a8 y = 2a  a2 = x y a2=(a8) 2a  a2=(a8) 2a a2+16a=0 a216a=0  p=1;q=16;r=0 D=q24pr=162410=256 D>0  a1,2=2pq±D=216±256 a1,2=216±16 a1,2=8±8 a1=16 a2=0  a=a1=16=16 m

Our quadratic equation calculator calculates it.

x=a8=168=8 m
y=2 a=2 16=32=32 m   Verifying Solution:  S1=a2=162=256 m2 S2=x y=8 32=256 m2

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