Unit 5 · Geometry
Square Divided into Four — Find the Perimeter
Lesson 1 of 4
When a square is split into identical rectangles, each small perimeter tells you the side lengths — work backwards from one rectangle to the whole square.
Sub-divided square perimeter items appear in the very-easy band of Selective MR — quick marks if you halve the rectangle perimeter to get one side of the square.
The examiner checks whether you can relate a small rectangle’s perimeter to its length and width inside a square, then scale up to the square’s perimeter.
A square is cut into four congruent rectangles. Each rectangle’s perimeter is given. You find the perimeter of the original square.
Best approach: Let the square side be s. Each rectangle is s × s/2 (or s/2 × s). Write 2(l + w) = given rectangle perimeter, solve for s, then perimeter of square = 4s.
Question
A square is divided into four identical rectangles. Each rectangle has a perimeter of 120 cm. What is the perimeter of the square?
Select an answer to see the explanation.
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