F.2 algebra

Question

The organisers of s fair deciede to create a temporary parking lot in a field. There are enough stakes and rope for 270m of fencing. An entrance and exit are required, each 5m wide. The edge of the field is to be used for one side of the parking lot. Draw and label a design for the parking lot, creating as much area for cars as possible.

Answer 1

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───────────────── → The edge of the field

|....................................... 5 << Entrance

|........................................|

|........................................|

W = 70 ...........................60

|........................................|

|........................................|

|____________________5 >> Exit

............ L = 140 Let L be the length and W be the wide of the temporary parking lot ,then 2W + L - 2(5) = 270

L = 280 - 2W

The area for cars

= W L

= W (280 - 2W)

= - (2W² - 280W)

= - 2(W² - 140W)

= - 2(W² - 2(70)W + 70² - 70²)

= - 2( (W - 70)² - 4900 )

= 9800 - 2(W - 70)²

When W = 70 , the maximum area for cars = 9800 m².

(L = 280 - 2W = 140)