From Words to Formula: Rectangle Perimeter

What you do

You shape the function y = 2*(x + b) and watch the graph answer.

Challenges to clear

• A rectangle has length x = 3. Slide the breadth b until the perimeter y is 16. (Watch the x = 3 row in the table.)
• Keep that same b. The rule must work for EVERY length: check that x = 7 now gives perimeter 24.
• A frame again, but now BOTH numbers are yours to find. The breadth is 4 — slide b there.
• Now how many lengths go round the frame? Slide a until a length of 3 gives a perimeter of 14. A rectangle has two lengths, not one.

Check yourself

Why does the perimeter formula y = 2*(x + b) multiply (x + b) by 2?

With b = 5 and x = 3, the rule gives 2*(3 + 5) = 16. Which other calculation gives the SAME perimeter?

• Walking around a rectangle covers the length twice and the breadth twice. — correct
• Because a rectangle has two diagonals.
• Doubling makes the answer easier to read in the table.
• Because only the length x gets doubled, not the breadth.
• 2*3 + 2*5 — correct
• 3 + 5
• 2*3*5
• 3*5 + 2

Think about it

• The rule is y = 2*(x + b): add length and breadth, then double. If b = 5 and the length x = 3, what perimeter y do you expect? Check the table.