76. Rectangle's Perimeter Race · 2 times (length + breadth)

Try to break it

Drag B to change the length and D to change the breadth. The perimeter always equals 2(l+b). Try to make it different!

How you build it

Construct a rectangle.

• Place point A, the first corner of the rectangle.
• Place point B. The segment AB will be the base of the rectangle.
• Draw the base segment from A to B.
• Construct a line through A, perpendicular to AB — this line is the side AD.
• Construct a line through B, perpendicular to AB — this line is the side BC.
• Mark point C on the perpendicular at B, above AB. The height of C sets the height of the rectangle, and BC is the second side.
• Set the compass opening to BC — click B, then C. This stores the height of the rectangle.
• With the same opening, draw an arc centred at A — it crosses the perpendicular at A.
• Mark point D where the arc crosses the perpendicular at A, above AB. Now AD = BC — the two sides are equal.
• Draw the top side from D to C. ABCD is a rectangle — opposite sides equal, all angles right angles.

The proof, step by step

Prove that the perimeter of a rectangle is 2 × (length + breadth).

• The perimeter of a rectangle is the sum of the lengths of all four sides.
• In a rectangle, opposite sides are equal. So, AB = CD = l and BC = DA = b.
• Perimeter P = AB + BC + CD + DA = l + b + l + b = 2l + 2b = 2(l + b).

Worked example

A rectangular park is 150 m long and 80 m wide. What is its perimeter?

P = 2(l + b) = 2(150 + 80) = 2(230) = 460 m.

• 230 m
• 460 m — correct
• 12000 m
• 310 m