Study guides › Level 6 · Master

A rectangle from its area and perimeter

Level 6 · Master · for questions like “A rectangle has an area of 24 sq m and a perimeter of 22 m. How long is the longer side?”

💡 The idea

• Perimeter = 2 × (length + width), so length + width = perimeter ÷ 2.
• Area = length × width.

You need two numbers that add to half the perimeter and multiply to the area.

🪜 The steps

1. Halve the perimeter.
2. List the pairs that multiply to the area.
3. Pick the pair that adds to the half-perimeter.

✏️ Worked examples

1. Area 24, perimeter 22: the sides add to 11. Pairs for 24: 1 & 24, 2 & 12, 3 & 8, 4 & 6. Only 3 & 8 add to 11, so the longer side is 8 m.

2. Area 36, perimeter 30: the sides add to 15. 3 & 12 works, so the longer side is 12 m.

⚠️ Watch out

• Halve the perimeter first. The two sides add to 11, not 22.

🎯 Try these

1. Area 20, perimeter 18: the longer side?
2. Area 40, perimeter 26: the longer side?
3. Area 48, perimeter 28: the longer side?

Answers: 1) 5 2) 8 3) 8 (6 & 8)

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.