Area

[Sissy Devane]

The length of a rectangle is twice the width. The area is 32yd^2. Find the length and the width?
I know that the formula for the area of a rectangle is
2L + 2W = A
so therefore, 2L + 2(2W)= 32yd^2
I need help...PLease

 

[mmm4444bot]

Hi Sissy D:

You're using the formula for the perimeter of a rectangle, not the area.

A = L * W

Also, you substituted the expression 2W for W (i.e., you proceeded as if the width equals twice the width). The variable L represents the length.

The first sentence in this exercise tells us the following.

L = 2W

In the area formula above, replace the variable L with the expression 2W.

Replace the variable A with the constant 32.

NOTE: We don't generally write any units of measurement (eg: yd^2) in our equations. Report the units with the final answer, instead.

Expand the righthand side.

Divide both sides by 2.

Take the square root of both sides.

Interpret the results.

Cheers,

~ Mark

 

[Sissy Devane]

ok I am lost but here is what I understand
32^2 = 1024
1024 = 2w * w
1024 = 2w^2
then I take the sqrts
32=w which is the width
and
2 * 32 = 64 which is the length

Is this correct?

 

[mmm4444bot]

1024 = 2w^2
then I take the sqrts
32=w which is the width

32 yd^2

This means that the area is 32 square yards.

Neither the abbreviation "yd^2" or the word "square" above is an instruction to square anything. Area is measured in square units. The area is 32 square yards, not 1024 square yards.

I instructed you to replace the variable A with the constant 32. I did not instruct you to square one side of the equation.

32 = 2w^2

I will now repeat the instructions I previously posted. If you do not understand the instructions, then please ask specific questions.

Divide both sides by 2.

Take the square root of both sides.

Interpret the results.

Cheers,

~ Mark

 

[Sissy Devane]

okay...I am trying to learn this

32= 2w^2
12 = w^2
2 sqrt 3 = w
this is the answer I come out with

 

[Mrspi]

okay...I am trying to learn this

32= 2w^2
12 = w^2<----if 32 = 2w[sup:19ewscxh]2[/sup:19ewscxh], how do you get 12 = w[sup:19ewscxh]2[/sup:19ewscxh]????
2 sqrt 3 = w
this is the answer I come out with

If you divide both sides of

32 = 2w[sup:19ewscxh]2[/sup:19ewscxh] by 2, you should get

16 = w[sup:19ewscxh]2[/sup:19ewscxh]

Now take the square root of both sides to find w.

And check in the original problem to see if it works.

 

[Sissy Devane]

Thank you for your patience and the advice

16 = w^2
4 = w
This this the width, the lenght is twice the width so the lenght would equal 8
I sure hope I finally have this problem right?

 

[mmm4444bot]

4 = w
This this the width, the lenght is twice the width so the lenght would equal 8

Yes, this is correct.

Most teachers like to see the final answer reported using a complete English sentence with units.

"The rectangle is 8 yards long and 4 yards wide."

"The length is 8 yards, and the width is 4 yards."

"The rectangle's dimensions are 8 yards by 4 yards."

It seems probable (to me) that you need to review some basics: Understand the difference between area and perimeter; understand the difference between a unit and a square unit; understand why you first thought that 32/2 was 12; understand what symbols represent, before you start substituting or manipulating them.

Cheers