Unit 5 · Geometry
Rectangular Flower Bed — Area and Ratio
Lesson 1 of 6
Let's start with one of the most common geometry setups in OC MR: a shape where the perimeter is given and one dimension is a fixed multiple of the other. The goal is to find the area — which means first recovering the two dimensions from the perimeter using a single variable.
Ratio-based perimeter-to-area questions appear in almost every OC MR paper, usually in the first half. They are reliably easy marks for students who know to introduce one variable for both dimensions — and a common trap for those who try to guess or trial-and-error.
The examiner is checking whether you can set up a simple algebraic equation from P = 2(l + b), substitute the ratio relationship, solve for the unknown, and then correctly multiply the two dimensions to get the area — rather than confusing perimeter with area.
A rectangle is described with its perimeter and a length-to-breadth ratio (e.g. length is twice the breadth, or length is 3 more than breadth). You must find the area. The numbers are chosen so that trial-and-error with the options is slow — one-variable algebra is the fastest path.
Best approach: Let breadth = b. Express length in terms of b using the ratio. Substitute into P = 2(l + b) and solve for b. Then calculate l. Finally, area = l × b. Four steps, no guessing needed.
Question
A rectangular flower bed has a perimeter of 9.6 m. If its length is twice its breadth, what is its area?
Select an answer to see the explanation.
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