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