Can anyone tell me if this correct? Thanks?

Question

The lenght of a rectangle is twices the width, the perimeter is 42 inches find the width. Answer w=4
The length of a rectangular picture is secven inches longer than the width. find the length and width if the perimeter of the picture is 62 inches?Answer

Answer 1

Problem 1

Perimeter formula

P = 2L + 2W

42 = 2(2W) + 2W

42 = 4W + 2W

42 = 6W

42 / 6 = 6W / 6

42 / 6 = W

7 = W

The width is 7 inches

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Problem 2

P = 2L + 2W

62 = 2(w + 7) + 2w

62 = 2w + 14 + 2w

62 = 4w + 14

62 = 14 = 4w + 14 - 14

48 = 4w

48 / 4 = 4w / 4

48 / 4 = w

12 = w

The width is 12 inches

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Answer 2

For the first exercise... Length=twice width ---> L=2*W
Perimeter=Sum of Sides ---> Per=L+L+W+W
Replace L for 2*W -----> Per=(2*W)+(2*W)+W+W
Per=6*W .. (You know perimeter is 42 inches)
42=6*W ----> W=42/6 ----> W=7 inches
and if you want to know the length L=2*W = 2*7= 14 inches

Second Exercise .. L=W+7 inches
Perimeter=L+L+W+W (Replace L for W+ 7)
Per=(W+7)+(W+7)+W+W
Per=(4*W)+7+7 ---> Per=(4*W)+14
You know Per=62 inches so replace
62=(4*W)+14
62-14= (4*W) ---> 48=4*W
48/4=W -----> W=12 (here's your width)
To find the length replace in L=W+7 ----> L=12+7 --> L=19

Answer 3

1 ) Let the width = x. Then length = 2x

Now, perimeter = 2x + x + 2x + x = 6x = 42

which gives width x = 7 in.

2 ) Let the width = x. Then length = x + 7

Now perimeter = x + 7 + x + x + 7 + x

= 4x + 14 = 62 which gives

width x = 12 in.

Answer 4

2 * x + 2(2x) = 42

2x + 4x =42

6x =42

x =42/6 = 7

so the width should be 7 and the length is 14



L = w + 7
2L +2 w = 62

this is solved by

2w + 14 + 2w = 62
thus
4w + 14 = 62
4w + 14 - 14 = 62 - 14
4w = 48

w = 48/4 = 12
and
L = 12 + 7 =19


so w = 12 and L = 19

Answer 5

The first one is wrong. Here's how to solve it:
Say that L=lenght and W= width and P=perimter
The formula to get the perimeter of a rectangle is 2L+2W=P
We know that P=42 and L=2W
So....
2(2W)+2W=42

Which can be simplified to....
4W+2W=42

Which can again be simplified...
6W=42

Now divide both sides by 6. This leaves you with...
W=7

So the width equals 7.

Here's the answer for the second problem.
Again, we use the same formula: 2L+2W=P
But now we know that P=62 and L=W+7.
So....
2(W+7)+2W=62

Which can be simplified to....
2W+14+2W=62

Now simplify to....
4W+14=62

Subtract 14 from both sides...
4W=48

Divide both sides by 4.
W=12

The lenght is equal to W+7, so....
12+7=L
L=19
So the lenght is 19 and the width is 12.


To double check any of these answers, just plug the answers into the formula. I hope that helps.

Answer 6

w=7

Answer 7

the first ones ans = width = 7inches(2(2x+x)=42; 6x= 42;x=7)

2(7+x(length)+x)= 62
14 + 4x=62
4x = 48
x= 12 inches
length = 19 inches
width = 12 inches

Answer 8

2l+2w = 62
l = w+7
2w+2w+14=62
4w+14=62
4w=48
w=12
l=w+7=19

2*19+2*12=38+24=62

Answer 9

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Answer 10

let w=x,length=2x
perimeter=2(x+2x)=6x
6x=42
x=7''w=7''
so w=4 is wrong.
2.let w=x,length=x+7
perimeter=2(x+x+7)=4x+14
4x=14=62
4x=48
x=12''=width, length=19''.answer