Question

Jordan has 30 meters of the border to create his classroom bulletin board. He wants to create the largest area possible.
Which dimensions will give Jordan the largest area?

Answer 1

Given:

Bulletin board of perimeter 30 m.

To find:

The dimensions of the board which gives the largest area.

Solution:

1) We know that the shape of the board must be rectangle which have the length and the breadth.

2) The perimeter of the board given in the question is 30 m so the sum of the dimension is 15m.

3)Let the length= x and breadth = 15-x so the area would be x(15-x) m².

4)To find the maximum area we will find the first derivative of area and put it equal to zero.

• derivative of(15x - x²) = 0

• 15 - 2x = 0

• x = 7.5 m

• (15-x) = 7.5 m

5) Which gives the area= L×B = 7.5×7.5 = 56.25 m² that is maximum from all the possibilities.

The largest possible area is 56.25 m².