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Simple Optimisation Question

I need help with this question. Thanks for any replies!...

...A rectangular field is x metres long. It is enclosed by 200 metresof fencing.

(a) Find an expression in terms of x for the breadth of the field.

(b) Hence find the greatest area which can be enclosed with the 200 metres offencing.

Reply 1

joostan

Original post by Lewis.G

What have you tried so far?

Reply 2

Kiddarion

a) As the field is x metres long (that's the length) and perimeter is 2l+2b and perimeter is 200 cos that's the amount of fence enclosing the field, 200=2l+2b. Sub l=x so 200=2x+2b then rearrange for b to get b=100-x
b) To get the biggest area you want a square as squares with same perimeter have bigger areas (eg when sides are 5&5 area =25 when sides are 6&4 area =24 but same perimeter) so since 200=2l+2b that means 100=l+b so if it was a square the length and breadth would be 50 each so area is 50*50=2500
Hope this helps

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