Find the dimensions of the rectangle of maximum area that can be formed from a 210-in. piece of wire.

  52.5 inch square

Step-by-step explanation:

The maximum area of any polygon for a given perimeter is the area of a regular polygon. Here, the polygon is a quadrilateral. The regular quadrilateral is a square, and each side length is 1/4 of the perimeter.

  (210 in)/4 = 52.5 in

The rectangle of maximum area is a square of side length 52.5 inches.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for