you can think this
WL = 28
L=3w + 8
W( 3W +8) = 28
3 W^2 + 8W + = 28
3W^2 + 8W -28 = 0 (1)
3 W^2 - 6 W + !4 W -28 =0-
3 W ( W - 2 ) + 14 ( W -2) =0
(3W+ 14) ( w-2) = 0
w = 2 L = 3(2) + 8 = 14 , then LW =28
ignore the negative answer of w = -14/3
If we write all factors of 28 { 2, 4 , 7, 14)
We see that 28 = 2 * 14 , 14 = 2* 3 + 8
Therefore we can have a rectangle with area of 28 units, with 2, 14 be its dimension , and have the
property of L = 2*3 +8 (
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Nicole B. answered • 01/18/14
TUTOR 4.9 (82)
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Hi Victoria,
Area=Length x width= 28 sq in
L=8+3w
So substitute that back into the equation:
Area = L x W
28 sq in = (8+3w) x w
28 sq in = 8w +3w2
28 sq in = w (8 + 3w)
Possible factors of 28 are 2 and 14 or 4 and 7, and 1 and 28. Substituting the possibilities in the equation, we find that the correct set of factors are 2 and (8 + 3*2) or 14.
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Arthur D. answered • 01/18/14
TUTOR 4.9 (67)
Mathematics Tutor With a Master's Degree In Mathematics
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w=width
l=3w+8
A=l*w
28=(3w+8)(w)
28=3w^2+8w
3w^2+8w-28=0
(3w+14)(w-2)=0
3w+14=0
3w=-14
w=-14/3, disregard this answer because it is negative
w-2=0
w=2
l=3*2+8
l=14
check: 28=14*2=28
l=14 inches
w=2 inches
14 is 8 more than 3 times 2 !
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Tom D. answered • 01/18/14
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Very patient Math Expert who likes to teach
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1) A=LW = 28 in
2) L = 3W + 8
Substitute L = 28/W into the 2nd equation
28/W = 3W + 8
28 = 3W^2 + 8W
3W^2 + 8W - 28 = 0
(3W+ 14)(W - 2) = 0
Note that the answer must be positive therefore the second 'zero' is the answer
