Fraction Classroom · 2.6.0 · Student pages

Recover a missing rectangle side and check the boundary

Use area and one known side to recover a missing dimension, then test whether the complete rectangle meets a separate perimeter limit.

Anonymous group code: __________ Date: __________

The area fixes the missing side when one side is known. A separate perimeter calculation tests the 30 cm edging limit.

Start with a diagnostic

diagnostic. A rectangle covers 20 square cm and one side is 4 cm. What is the other side? Write a multiplication equation with a missing factor before solving it.

Build the idea

model. A rectangular display must have area 48 square cm and width 6 cm. At most 30 cm of edging is available. What length is required, and does its complete boundary fit the edging limit?

Sketch a rectangle, label its known 6 cm width and write 6 × unknown length = 48. The area counts square-centimetre units; the missing side must be a length in centimetres.
Divide the area by the known side: 48 ÷ 6 = 8 cm. Label the opposite sides 8 cm and the remaining opposite side 6 cm, then verify 6 × 8 = 48 square cm.
Trace the whole boundary and record 8 + 6 + 8 + 6 = 28 cm, or 2 × (8 + 6) = 28 cm. Adding just one length and one width counts only half the boundary.
Compare the calculated 28 cm boundary with the separate 30 cm limit. It fits, with 30 − 28 = 2 cm left. The decision uses both the required area and the available edging.

Worked example: The length must be 8 cm because 48 ÷ 6 = 8. The perimeter is 2 × (8 + 6) = 28 cm, so the rectangle meets the 30 cm limit with 2 cm of edging left.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. Support: a rectangle has area 24 square cm and width 4 cm. Enter its missing length in cm. Draw four-square rows and check the completed area equation.

p2. Core: a rectangle has area 54 square cm and width 6 cm. Recover its length, then enter its complete perimeter in cm. Label all four sides on your sketch.

p3. Challenge: a rectangular plan requires area 36 square cm and width 4 cm, with at most 24 cm of edging. Enter how many extra centimetres of edging the required rectangle would need, and explain whether the plan meets all constraints.

e1. Independent check: a rectangle must cover 60 square cm and have width 5 cm. The edging limit is 34 cm. Enter the missing length in cm, then show the area check, complete perimeter and a decision about the limit.

Transfer the idea

transfer. A proposed repair to the worked plan uses length 7 cm and width 6 cm. Its author says the 26 cm perimeter is below the 30 cm limit, so it must meet the plan. Does it satisfy every requirement?