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Rectangle Perimeter with Ratio
The length and width of a rectangle are in the ratio 5:3. If the perimeter is 64, what is the area of the rectangle?
Need a hint?
Let the length be 5k and the width be 3k.
Correct answer
C. 240
Solution
Let:
Length = 5k
Width = 3k
The perimeter is:
2(5k + 3k) = 64
2(8k) = 64
16k = 64
k = 4
So:
Length = 20
Width = 12
Area:
20 × 12 = 240
Detailed solution
The perimeter gives the sum of length and width indirectly. Since 2(L + W) = 64, the value L + W is 32. The ratio parts 5k + 3k equal 32, giving k = 4.
Common mistake
A common mistake is treating 64 as L + W instead of the full perimeter.
Trap logic
The trap is forgetting to divide the perimeter by 2.
What this reveals
If this was missed, the issue may be formula setup, not area calculation.
StudyGlitch notes
GAT geometry questions often combine ratio and shape formulas.
For rectangle ratio problems, translate the ratio into variables, then use the perimeter formula carefully.
Remember: perimeter of rectangle is 2L + 2W, not L + W.
This week’s question is more than a score.
A wrong answer usually points to a pattern: slow recognition, a trap choice, weak setup, or pressure under time. Use this challenge as a signal, then connect it to your diagnostic, practice history, and weekly StudyGlitch progress.