Thread: quadratic algebra

a farmer has 60m of fencing with which to construct three sides of a rectangular yard connected to an existing fence.
a. if the width of the paddock is x m and teh area inside the yard, A m^2, write down teh rule connecting A and x
b. determine teh maximum area that can be formed for the yard.

( the side of existing fence is a length)

please help me i have an exam tomorrow on this!!!

Originally Posted by summna09

a farmer has 60m of fencing with which to construct three sides of a rectangular yard connected to an existing fence.
a. if the width of the paddock is x m and teh area inside the yard, A m^2, write down teh rule connecting A and x
b. determine teh maximum area that can be formed for the yard.

( the side of existing fence is a length)

please help me i have an exam tomorrow on this!!!

Hello,

a) first make a sketch of the situation.

Since the length of the fence is 60 m the length of the rectangle is:



You are supposed to know that the area of a rectangle can be calculated by



b) . A is a quadratic function pointing down, that means the maximum value is at it's vertex:
In general the x-value is calculated by: With your problem:


Thus the rectangle has the dimension: