NCERT Solutions for Class 5th Maths Chapter 11 Does a bigger area always mean a bigger perimeter? — Trisha's Two Rectangles
Book page 147 Updated on2026-09-19
Q1.
Trisha makes these two rectangles. She says, “I increased the area of my rectangle, and the perimeter increased.” Do you think this is always true?
Answer
No, it is not always true. It happened for Trisha's two rectangles, but you can easily find a pair where the area grows and the perimeter shrinks.
First check Trisha's own rectangles.
Trisha is right about her own two rectangles — both numbers went up.
First rectangle: area = 2 × 3 = 6 square units, perimeter = 2 + 3 + 2 + 3 = 10 units Second rectangle: area = 3 × 4 = 12 square units, perimeter = 3 + 4 + 3 + 4 = 14 units Area went 6 → 12 (up) and perimeter went 10 → 14 (up)
Now here is a pair where her rule breaks.
The second one has MORE area but LESS perimeter. Trisha's rule is not always true.
Long thin rectangle 8 × 1: area = 8 square units, perimeter = 8 + 1 + 8 + 1 = 18 units Square 3 × 3: area = 9 square units, perimeter = 3 + 3 + 3 + 3 = 12 units Area grew from 8 to 9, but perimeter fell from 18 to 12
Why area and perimeter do not have to move together: Perimeter is about the edge. Area is about the inside. A long thin strip has a huge edge and very little inside. A fat, square shape has a short edge and a lot of inside. So changing the shape can push the two numbers in opposite directions.
What is true: If you add squares to a rectangle without changing its width — as Trisha did — the area must go up, and the perimeter goes up too. Trisha's mistake is only in the word always.