Miles has a square garden in his backyard. He decides to decrease the size of the garden by 1 foot on each side in order to make a gravel border. After he completes his gravel border, the area of the new garden is 25 feet2. In the equation (x - 1)2 = 25, x represents the side measure of the original garden. Whats the length and area?
Let
x-------> the length side of the original square garden
Step 1
Find the value of x
we know that
\((x-1)^{2}=25\)
taking square root both sides
\((x-1)=(+/-)\sqrt{25}\)
\((x-1)=(+/-)5\)
\(x1=1+5=6\ ft\)
\(x2=1-5=-4\ ft\)
the solution is
\(x=6\ ft\)
therefore
the answer Part a) is
The original length side of the square garden is \(6\ ft\)
Step 2
Find the area of the original square garden
we know that
the area of the original square garden is equal to
\(A=x^{2}\)
substitute the value of x in the formula
\(A=6^{2}=36\ ft^{2}\)
therefore
the answer part b) is
the area of the original square garden is \(36\ ft^{2}\)