How many different areas in square inches can the rectangle have?

The perimeter of a rectangle is 22 inches and the inch-measure of each side is counting number. How many different areas in square inches can the rectangle have?

MetroEye: The perimeter of a rectangle = 2(l+b) where l is length and b is the breadth of rectangle. The area of the rectangle = l*b.

Given 2(l+b) = 22

=> l+b = 22/2 = 11 inches.

Each side i.e; l and b are counting numbers which when added should give 11.

So the options are,

l	b	l*b
1	10	10
2	9	18
3	8	24
4	7	28
5	6	30

Rectangle can have 5 different areas.

What is the largest number of sections of the rectangle?

In the rectangle at the right, line segment MN separates the rectangle into 2 sections. What is the largest number of sections into which the rectangle can be separated when 4 line segments are drawn through the rectangle?

When no lines are added, there is only one segment.
When one line is added, the number of segments is 2.
When two lines are added, the number of segments becomes 4.
When three lines are added, the number of segments becomes 7.

Observing the pattern, each time a line is added, that many segments gets added to the number of segments formed.

i.e; when three lines are added, it will be 4+3=7
So according to the pattern, when four lines are added, the number of segments = 7+4=11

Largest of number of sections into which the rectangle can be separated when 4 line segments are drawn is 11.

How many inches are in the perimeter of the U-shaped figure?

The U shaped figure at the right contains 11 squares of same size. The area of the U-shaped figure is 176 square inches. How many inches are in the perimeter of the U-shaped figure?

Area of 11 squares = 176 sq inch
Area of 1 square = 176/11 = 16 sq inch

Area of a square = square of its side
=> Side of the square = \(\sqrt{16}\) = 4 inches



Outside- Perimeter of the figure = 4*4+5*4+4*4+2*4 = 60
Inside - Perimeter of the figure = 3*4+3*4+3*4= 36

Perimeter of the U shaped figure = 60+36 = 96 inches