Question

What is the largest possible area (in cm²) for a rectangle with a perimeter of 120 cm?

Answer 1

Answer:

900 cm²

Step-by-step explanation:

Perimeter of a rectangle is given by

P=2(l+w)

Where l and w are length and width respectively.

Substituting P with 120 cm

120=2(l+w)

Divide both sides by 2

60=l+w

Making w the subject of formula

w=60-l

Area, A=lw

Substitute w with 60-l

A=l(60-l)=60l-l²

Since A=60l-l²

Get the first derivative of A with respect to l

0=60-2l

l=60/2=30

Therefore, w=60-l=60-30=30

The length abd width are both 30cm. This is a square and a square is also a type of rectangle since it has four sides.

Area=30*30=900cm²