Among all rectangles with a fixed perimeter P, which shape has the maximum area?

Model Answer & Options

Source: Extra Practice

A rectangle with length twice the width

A square

A rectangle with width very close to zero

Area is constant for all rectangles of same perimeter

Explanation

Let sides be x and y. Perimeter P = 2(x+y), so y = (P/2) - x. Area A = xy = x(P/2 - x) = (Px/2) - x². To maximize area, dA/dx = P/2 - 2x = 0, which gives x = P/4. Since x = P/4, then y = P/2 - P/4 = P/4. Because x = y, the rectangle is a square.

Try a Related Quiz

Test your skills on a similar concept: Units and Measurement - NCERT Class 11 Practice Set 1.

Start Related Quiz

Explore the Full Topic

This is just one question from the topic "Maxima and Minima".

View All Questions

Related Questions