Answer:
Perimeter of a rectangle is given by:
\(P= 2(L+W)\) .....[1]
where
P is the perimeter of a rectangle
L is the length of the rectangle
W is the width of the rectangle.
As per the statement:
A rectangular garden has a perimeter of 172 feet.
⇒P = 172 feet
It is also given that:
The length of the garden is 24 feet more than the width.
⇒\(L= 24+W\)
Substitute the given values in [1] we have;
\(172=2(24+W+W)\)
Combine like terms;
\(172=2(24+2W)\)
Divide both sides by 2 we have;
\(86=24+2W\)
Subtract 24 from both sides we have;
\(62=2W\)
Divide both sides by 2 we get;
31 feet = W
Then;
\(L= 24+31 = 55\) feet.
therefore, the dimension of the garden are:
\(L= 55\) feet and W = 31 feet
