For rectangles of area 100 m^2 what is the perimeter of the rectangle with the smallest perimeter?

100=ab

P=2a+2b

P=2a+200/a

dP/da=2-200/a^2

dP/da=0 implies 2=200/a^2

a^2=100

a=-10,10

a is a length so take positive a, a=10

so b=10

gives perimeter 40m

Notice a=10 b=10 is a square

Squares are rectangles of smallest perimeter

DN
Answered by Daniel N. Maths tutor

11063 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How would you differentiate and integrate 2x^3?


A curve has equation y = 20x −x^2 −2x^3 . The curve has a stationary point at the point M where x = −2. Find the x-coordinate of the other stationary point of the curve.


Express x^2-4x+9 in the form (x-p)^2+q where p and q are integers


Find the derivation of (sinx)(e^2x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning