How do i get this stupid formula? and i know you can solve it too?

Question

The width of a rectangular window frame is 12 inches less than its length. If you add 30 inches to both the length and width, you double the perimeter. Find the length and the width of the original rectange

Answer 1

I'll tell u this: L+W= -16

Answer 2

W = width

L = length

W = L - 12

P = perimeter = 2*W + 2*L = 2*(L - 12) + 2*L = 4L - 24

W + 30 and L + 30 gives a perimeter of 2P so:

2P = 2(W + 30) + 2(L + 30) = 2W + 2L + 120

2P = P + 120 ..... since 2W + 2L = P

P = 120

Now find L and W.

P = 2W + 2L = 2*(L - 12) + 2*L = 4L - 24 = 120

4L = 120 + 24 = 144

L = 36 and W = L - 12 = 24

Check: P = 2W + 2L = 2(36) + 2(24) = 72 + 48 = 120 which is right

Now when we add 30 to L and W:

W = 24 + 30 = 54

L = 36 + 30 = 66

P = 2W + 2L = 2(54) + 2(66) = 108 + 132 = 240

And this is double the original perimeter which is what we want.

So the original length is 36 inches and original width is 24 inches

Note. Veck should have put parenthesis around L + 30 and W + 30. he should also check his answer and then he would know that he made a mistake.

Answer 3

P = 2l + 2w

2l + (2(l - 12)) = (2l + 30) + (2(l - 12) + 30)/2

2l + 2l -24 = 2l + 30 + 2l -24 +30/2

4l - 24 = 4 l +36/2

4l - 24 = 2l +18

-2l from both sides

2l - 24 = 18

+24 to both sides

2l = 42

divide both sides by 2

l = 21

length = 21

w = l -12

w = 21 - 12

w = 9

width = 9

Answer 4

W = L - 12

2(W +30) + 2(L + 30) = 4W + 4L

Substitute from there

2((L - 12) + 30) + 2(L + 30) = 4(L - 12) + 4L

2(L + 18) + 2L + 60 = 4L - 48 + 4L

2L + 36 + 2L + 60 = 4L - 48 + 4L

4L + 96 = 8L - 48

4L = 8L - 144

-4L = -144

L = 36

W = 36 - 12 = 24

Sorry, I did make a mistake, I apologize for any confusion.

I corrected above

Answer 5

The width of a rectangular window frame is 12 inches less than its length. If you add 30 inches to both the length and width, you double the perimeter. Find the length and the width of the original rectange

Meg B Hi !!

Given:

Length = L

Width = W = L + 12 ← eq 1

Perimeter Org = Po = WL ← eq 2

Condition Perimeter

2Po = (W + 30)(L + 30) ← eq 3

Substitute eq 2 to eq 3

2(WL) = (W + 30)(L + 30) ← eq 4

Substitute eq 1 to eq 4

2[(L + 12)L = [(L + 12) + 30][L + 30]

2L² + 24L = [L + 32][L + 30]

2L² + 24L = L² + 30L + 32L + 960

Transposing

2L²  + 24L - L² - 30L - 32L - 960 = 0

Combining terms

L² - 38L - 960 = 0

Quadratic

a=1  b=(-38)  c=(-960)

L= [-b ±√b²  -4ac]/2a

L= [38 ±√1444  - 4(-960)]/2

L= [38 ±√5284]/2

L= [38 ± 72.69]/2

L+ = [38 + 72.69]/2

L+ = 55. 35 in

L- = [38 - 72.69]2

L- = - 17. 35 in

From eq 1 :  W = L - 12

W = 55.35 - 12

W = 43.34 in

Summary

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Ans::: L = 55.35 in  &  W = 43.35 in

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hope this helps