a table top is rectangular. the table's length is 60 cm more than its width. the perimeter of the table is 240 cm.

## find the length and width of the table

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# 6 Answers

Dear Travina,

1. We know that the table's length, L, is 60 cm greater than its width, W.

2. We know that the perimeter, P, is 240 cm.

The equation is very simple:

P = 2*L + 2*W

But we already know that L = W + 60 cm

So rewrite the equation for the perimeter as:

P =2*(W + 60 cm) + 2*W

P = 240 cm = 2*W + 120 cm + 2*W

4*W = 240 cm - 120 cm = 120 cm

Therefore W = 30 cm.

So, the rectangular table has a length, L, of 90 cm and a width, W, of 30 cm.

Let's check our answer:

P = 2*L + 2*W = 2*(90 cm) + 2*(30 cm) = 180 cm + 60 cm = 240 cm.

We will call the width x cm...making the length x + 60 cm. There are 4 sides, 2 widths and 2 lengths, which equal 240 cm.

SO, x + x +(x + 60) + (x + 60) = 240

SO, x + x +(x + 60) + (x + 60) = 240

4x + 120 = 240

4x = 120

x = 30 cm (width)

x + 60 = 90 cm (length)

Hi again Travina;

Another great question!!!

Our first priority is to verify the fact that both measurements, 60 and 240, are presented in the same unit. In this circumstance, both are cm--good! Other questions may have one in cm and another in m. Please be careful!

perimeter=2(length + width)

length=width+60

x=width

240=2[(x+60)+x]

240=2x+120+2x

240=4x+120

Let's subtract 120 from both sides...

-120+240=4x+120-120

120=4x

Let's divide both sides by 4...

120/4=(4x)/4

30=x...width

90=30+60...length

Let's check our work...

perimeter=2(length+width)

perimeter=2(90+30)

perimeter=2(120)

perimeter=240

240=240

Perimeter = (2 x Length) + (2 x Width)

P = 2L + 2W

Here's the info you've been given:

L = W + 60

P = 240

Plug in the numbers:

240 = 2(W + 60) + 2W

Distribute the 2 to what's in the parenthesis:

240 = 2W + 120 + 2W

Combine like terms:

240 = 4W + 120

Subtract the 120 from both sides:

240 - 120 = 4W + 120 - 120

The goal is to get W all by itself, because once we know what W is, we can figure out what L is:

120 = 4W

Divide both sides by 4:

120/4 = 4W/4

Now we have W all by itself:

30 = W

If the Length is 60cm greater than the Width, and the Width is 30cm, then:

L = 30 + 60

L = 90

And just to double check, plug the numbers back into the original perimeter equation:

P = 2(90) + 2(30)

P = 180 + 60

P = 240

The length is 90cm and the width is 30cm. Ta-dah!

width=x

length=x+60

P=(2l)+(2w)

2(x+60)+2x=240

2x+120+2x=240

4x+120=240

4x=120

x=30

width=30

length=90

a table top is rectangular. the table's length is 60 cm more than its width. the perimeter of the table is 240 cm.

Establish some variables:

p - perimeter

l - length

w - width

The perimeter of a rectangle can be defined as:

p = 2l + 2w

And we are given:

l = w + 60

p = 240

So:

2l + 2w = 240

Substitute for length:

2l + 2w = 240

2(w + 60) + 2w = 240

2w + 120 + 2w = 240

4w + 120 = 240

4w = 120

w = 30

Now solve for l:

l = w + 60

l = 30 + 60

l = 90

Length is 90, and width is 30.

Double check by plugging those values into your equations:

p = 2l + 2w

240 = 2(90) + 2(30)

240 = 180 + 60

240 = 240