Questions on Word Problems: Geometry answered by real tutors!

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Question 149381: The length of a rectange is 6in more than 3 times its width. If the width were increased by 4 and the length decreased by 10, the area of the new rectangle would equal the area of the orignal rectangle. Find the length and width of the original rectangle.: The length of a rectange is 6in more than 3 times its width. If the width were increased by 4 and the length decreased by 10, the area of the new rectangle would equal the area of the orignal rectangle. Find the length and width of the original rectangle.
Answer by jojo14344(879) About Me  (Show Source):
You can put this solution on YOUR website!
Let A[old] = old Area , with following conditions:
L[length] = 3W+6
W[width] = W ,
So, A[old] = L*W ----> A[old] = (3W+6)(W)
A[old]= 3W^2 + 6W
.
Let A[new] = new Area with following conditions:
L[length] = 3W + 6 - 10 = 3W -4
W[width] = W+4
So, A[new] = L*W ----> A[new] = (3W-4)(W+4)
A[new] = 3W^2 + 8W -16
.
Equating the 2 Areas because of the conditions, becoming A[old] = A[new]
cross(3W^2) + 6W = cross(3W^2) + 8W -16 , rearranging thereafter:
8W - 6W =16 ----> 2W = 16
W = 8
Going back to the old condition for L= 3W + 6---> L= (3*8)+6
L= 30
In doubt? Go back A[old] = ((3*8)+6)(8)= 240
Also, A[new] = ((3*8)-4)(8+4)=240
A[old] = A[new]
Thank you,
Jojo
Question 149381: The length of a rectange is 6in more than 3 times its width. If the width were increased by 4 and the length decreased by 10, the area of the new rectangle would equal the area of the orignal rectangle. Find the length and width of the original rectangle.: The length of a rectange is 6in more than 3 times its width. If the width were increased by 4 and the length decreased by 10, the area of the new rectangle would equal the area of the orignal rectangle. Find the length and width of the original rectangle.
Answer by mangopeeler07(445) About Me  (Show Source):
You can put this solution on YOUR website!
l=3w+6------------------The length of a rectange is 6in more than 3 times its width
w=w---------------------The width
w(3w+6)=(w+4)(3w-4)-----------------If the width were increased by 4 and the length decreased by 10, the area of the new rectangle would equal the area of the orignal rectangle

Distribute
3w^2+6w=3w^2+8w-16

Subtract 3w^2 from both sides
6w=8w-16
Subtrat 8w from both sides
-2w=-16

Divide by -2
w=8

l=3w+6
w=w

Length=30
Widht=8