My friend has $225 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $10/meter on one side, and cheaper metal fencing w

Question

My friend has $225 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $10/meter on one side, and cheaper metal fencing which costs $5/meter for the other three sides.

What are the dimensions of the garden with the largest area she can enclose?
length for cedar side =
meter
width for other side =
meter

What is the largest area that can be enclosed?
area =
meter-squared

Answer 1

Since the maximum amount of siding for a set amount of money would be obtained by getting as little cedar as possible but (since the cedar side is given to be a 'length' side which implies it cannot be shorter than a 'width' side), the maximum would be a perfectly square garden. Therefore, if X is the length of one side,

10X + (3*5)X = 225 -> 25X = 225 -> X = 9

So, the area enclosed would be 9*9 or 81 m²