SAT Math in Dubai: model a change in a rectangle’s perimeter
A geometry word problem is easier to model when you separate what changes from what stays fixed. A percentage increase in perimeter does not automatically mean that each side increases by the same percentage.
This original exercise is useful for students preparing from Dubai or elsewhere. It is a teaching example, not an official SAT question or evidence of a particular student’s score improvement.
Draw and label the situation
A rectangular garden is initially 12 metres long and 8 metres wide. Its length is increased while its width remains 8 metres. The new perimeter is 20% greater than the original perimeter. What is the new length?
Write the old dimensions on one sketch and the new dimensions on another. The new width is known; call the new length L. This prevents the percentage from being attached to the wrong quantity.
Calculate the old and new perimeters
The original perimeter is 2(12 + 8) = 40 metres. A 20% increase gives a new perimeter of 40 × 1.20 = 48 metres.
Use the unchanged width in the new equation: 2(L + 8) = 48. Then L + 8 = 24, so L = 16 metres.
Check the model, not just the arithmetic
The new perimeter is 2(16 + 8) = 48, as required. The length increased by 4 metres, or one third of its original value; it did not increase by 20%. The perimeter change applies to the sum of the sides.
The area also changes differently: the old area was 96 square metres and the new area is 128 square metres. Those areas are not needed to answer the question, but their units help distinguish area from perimeter.
What your error tells you
- Using 12 × 1.20 treats the percentage as a change in length.
- Using 12 × 8 as the starting value substitutes area for perimeter.
- Changing both dimensions ignores the fixed-width condition.
- Giving 48 answers the perimeter rather than the requested length.
Geometry and Trigonometry is one of the SAT’s Math content domains. A total or section score cannot identify this specific weakness by itself; inspect your attempted work before choosing drills.
Try the free Math Skills Check for further original practice, or discuss your setup with an online SAT tutor for Dubai. A high target score is a planning goal, not a guaranteed result from a fixed number of geometry sessions.