Question

The width of a rectangle is 33 centimeters. the perimeter is at least 776 centimeters.

what inequality expresses the length of the rectangle?
what is the area of the rectangle in square centimeters?

Answer 1

`x-\ length\\ width=33cm\\\\ Perimeter=2width+2length\\\\ 2x+2*33>776\\ 2x+66>776\ \ |Subtract\ 66\\2x>710\\\boxed{x>355cm}\\\\Area=width*length\\ Area>355*33\\ \boxed{Area>11715cm^2}`

Answer 2

Width of the rectangle is given to be 33 centimeters

Let the Length of the rectangle be x centimeters

So, Perimeter of rectangle is given by formula : Perimeter = 2 × (Length + Width)

⇒ Perimeter = 2 × (x + 33)

⇒ Perimeter = 2x + 66

Now, The perimeter of the rectangle is at least 776 centimeters

⇒ Perimeter > 2x + 66

⇒ 776 > 2x + 66

⇒ 2x < 710

⇒ x < 355

So, The length of the rectangle must be less than 355 cm

⇒ Area of the rectangle < 355 × 33

⇒ Area of the rectangle < 11715 cm²