Answer:
8
Step-by-step explanation:
<em> M = Original perimeter = 40</em>
<em> M = 2 w + 2 l = 2 ( w + l )</em>
<em> 40 = 2 ( w + l )</em>
Divide both sides by 2 (simplify)
<em> 20 = w + l</em>
<em> w + l = 20</em>
Subtract w from both sides
<em> w + l - w = 20 - w</em>
<em> l = 20 - w</em>
If the length is halved and the width is divided by 3 mean:
<em>New length l1 = l / 2 = ( 20 - w ) / 2 = 10 - w / 2</em>
<em> New width w1 = w / 3</em>
The new perimeter is decreased by 24 mean:
<em> P1 = New perimeter = 40 - 24 = 16</em>
<em> P1 = 2 w1 + 2 l1 = 2 ( w1 + l1 )</em>
<em> 16 = 2 ( w1 + l1 )</em>
Divide both sides by 2
8 = w1 + l1
w1 + l1 = 8
w / 3 + 10 - w / 2 = 8
Subtract 10 to both sides
w / 3 + 10 - w / 2 - 10 = 8 - 10
w / 3 - w / 2 = - 2
2 w / 6 - 3 w / 6 = - 2
- w / 6 = - 2
Multiply both sides by - 6
( - 6 ) ∙ ( - w / 6 ) = ( - 2 ) ∙ ( - 6 )
w = 12
l = 20 - w = 20 - 12 = 8
Proof:
Original perimeter:
<em>P = 2 w + 2 l = 2 ( w + l ) = 2 ∙ ( 12 + 8 ) = 2 ∙ 20 = 40</em>
New length:
<em>l1 = l / 2 = 8 / 2 = 4</em>
New width:
<em>w1 = w / 3 = 12 / 3 = 4</em>
New rectangle will be the square. ( the square is a special case of the rectangle )
New perimeter:
<em>P1 = 2 w1 + 2 l1 = 2 ( 4 + 4 ) = 2 ∙ 8 = 16</em>
The length of the original rectangle:
<u>l = 8</u>
<u>Answer 2</u>
