The length of a side of a rect is 6cm What should the length of the other side be so that the P of the rect is smaller than the P of a square with a side of 4cm

Question

Help me please I have a quiz on this in 1 hour!!

Answer 1

Let w = the width of the rectangle

Square: P = 4s

P = 4(4) = 16

Rectangle: P = 2l + 2w

2(6) + 2w < 16

12 + 2w < 16

2w < 4

w < 2 cm

Answer 2

Hi Marvin,

 

Draw a rectangle and label the long sides "6" and label the short sides "x".

The perimeter of this rectangle is now 6+x+6+x = 12 + 2x

 

The perimeter of a square with side of 4 cm is 4+4+4+4 = 16 cm

 

We need the perimeter of the rectangle (12 + 2x) to be smaller than (<) the perimeter of the square (16).

 

Here is the inequality that is needed:   12+2x<16

 

Solve this (subtract 12 from both sides)

 

2x<4

 

Divide both sides by 2

 

x<2.

 

So the other length your teacher is looking for must be SMALLER than 2 cm.