SOLUTION: Please solve this:
A retangular piece of wood is 12cm longer than it is wide. A strip 1cm wide is cut off all around. This decreses the area by 120 square cm. What were the origin
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Question 139124: Please solve this:
A retangular piece of wood is 12cm longer than it is wide. A strip 1cm wide is cut off all around. This decreses the area by 120 square cm. What were the original dimensions?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular piece of wood is 12 cm longer than it is wide. A strip 1 cm wide is cut off all around. This decreases the area by 120 square cm. What were the original dimensions?
:
Let x = width of the wood
then
(x+12) = length
:
Original area = x(x+12) = (x^2 + 12x)
:
Dimensions after the 1 cm strip removed
Width = (x-2)
Length = (x+12) - 2 = (x+10)
:
Area now: (x-2)(x+10) = (x^2 + 8x - 20)
:
The equation:
old area - new area = 120
(x^2 + 12x) - (x^2 + 8x - 20) = 120
:
x^2 + 12x - x^2 - 8x + 20 = 120
:
12x - 8x = 120 - 20
:
4x = 100
x =
x = 25 cm is the original width
then
(25 + 12) = 37 cm is the original length
;
:
Check solution by find the areas:
37*25 = 925
35*23 = 805
-----------
diff: = 120
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