Same area, different perimeter
Compare two rectangles that share the same area but have different perimeters. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Rectangle 1 measures 6 m by 8 m. Rectangle 2 measures 12 m by 4 m. Both rectangles have the same area. Which rectangle has the greater perimeter?
- Not enough information
- 12 m by 4 m
- 6 m by 8 m
- They have the same perimeter
Answer: 12 m by 4 m
See one solved, step by step
Rectangle 1 measures 5 cm by 12 cm. Rectangle 2 measures 15 cm by 4 cm. Both rectangles have the same area. Which rectangle has the greater perimeter?
- Not enough information
- 15 cm by 4 cm
- They have the same perimeter
- 5 cm by 12 cm
📘 Worked solution
1Area 1 = 5 · 12 = 60 cm2, Area 2 = 15 · 4 = 60 cm2Check that both rectangles really do cover the same area.
2Perimeter 1 = 2 · (5 + 12) = 34 cmAdd the length and width, then double it.
3Perimeter 2 = 2 · (15 + 4) = 38 cmDo the same for Rectangle 2.
4Answer: the 15 cm by 4 cm rectangleSame area, but a shape that is more stretched out (longer and thinner) has a bigger perimeter.
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