Use both a ratio and a geometric constraint
A ratio describes relative sizes; it does not by itself give their actual lengths. A second condition, such as perimeter, can fix the scale. For a rectangle, the perimeter is twice the sum of length and width. Do not confuse that sum with the perimeter or the perimeter with area. Worked example: a rectangle has width: length=2: 3 and perimeter 50 cm. Write width=2 k and length=3 k. Then 2(2 k+3 k)=50, so 10 k=50 and k=5 cm. The sides are 10 cm and 15 cm. Check both original conditions: 10:15 simplifies to 2: 3, and 2(10+15)=50. A result that passes one check but fails the other is not a solution. The diagnostic changes both the ratio and perimeter but uses the same taught method; it is the one diagnostic for this unit, not evidence of official question frequency. Make a small labeled sketch when the word length and the word width are easy to swap. Record linear units for perimeter and side length. An area answer would require square units and a different calculation. For a chosen equation, show why every term corresponds to a side rather than relying on a memorized operation with the total.
A rectangular display has width: length=3: 5 and a perimeter of 64 cm. What is its length?
- Write width=3 k and length=5 k. The perimeter is 2(3 k+5 k)=16 k=64, so k=4 cm and length=5×4=20 cm. Check: 2(12+20)=64 cm.
Compare the other answer choices
This is the width, 3×4, rather than the requested length.
This is the sum of width and length, not the longer side alone.
This treats 64 as width plus length instead of twice their sum.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which evidence or rule supports your decision and why the alternatives do not fit.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
LibreTexts—Perimeter and Circumference