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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
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