Yes, they are congruent. Same perimeter gives the same sum of sides and same area gives the same product. They share the identical quadratic equation, producing the exact same side lengths.
Two rectangles have the same area and the same perimeter. Does this mean that they are congruent to each other?
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Yes, they must be congruent.
Let the sides of a rectangle be x and y.
Perimeter = 2(x + y) = 2s, so x + y = s.
Area = xy = A.
Here, x and y are the roots of the quadratic equation:
t² – (x + y)t + xy = 0, which is t² – st + A = 0.
Since both rectangles have the same perimeter and area, their dimensions are solutions to the same quadratic equation.
Thus, their side lengths are identical, making the rectangles congruent.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/