Question

4. A rectangular plate has a perimeter of 28cm. determine the dimensions of the plate that give the maximum area​

Answer 1

Explanation:

The perimeter of a rectangle is the sum of its 2 widths and 2 lengths.

Lets call the width ‘W’ and the length ‘L’. The perimeter (P) is equal to 2W + 2L. So 28 = 2W + 2L which simplifies to 14 = W + L.

28/2=14

The area of a rectangle is the width multiplied by the length so the formula is A = W x L. We want to get rid of the length. So, if we rearrange the first equation 14 = W + L to make L the subject we get L = 14 - W. We can now substitute this into the area equation so we get → A = W x (14 - W). That’s your answer!