Need help please Geometry: Contrasting and relating the perimeter of shapes

Question

Anya wants to draw many different rectangles that have a perimeter of 16 cm. Anya draws a few rectangles, but then she stops drawing and starts looking for pairs of numbers that add to 8.

a. Why does it make sense for Anya to look for pairs of numbers that add to 8? How is she likely to use these pairs of numbers in drawing additional rectangles?

b. How could you adapt Anya’s idea if you were going to draw many different rectangles that have a perimeter of 14 cm?

Answer 1

a. The formula for perimeter is...

P = 2l + 2w

If we play around with that...

P = 2(l + w)

P/2 = l + w

If the perimeter is 16, that means the length and width add up to 16/2, aka 8.

b. Go!