A rectangular field has a length 10 feet more than it is width. If the area of the field is 264, what are the dimensions of the rectangular field?
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calendarEducator since 2009
write35,413 answers
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Let L be the length of the field. Let W be the width of the field. We know from your question that
L = W + 10
We also know that W*L = 264
This is because the area of a rectangle is equal to the length times the width.
So now we subsitute in
(W + 10)*W = 264
W^2 + 10W = 264
W^2 + 10W - 264 = 0
Now we have to find the factors. We can factor this out to
(w + 22) (w - 12) = 0
So the width could be -22 or 12. Of course it cannot be negative so
W = 12
and therefore
L = 22.
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Let us assume that the length is (L) and the width is (W)
We know that the area of a rectangle is a=L*W
==> LW = 264 ...(1)
But we know that L=W+10
Substitute with (1):
(W+10)W =264
w^2 + 10w = 264
w^2+10w -264=0
Factorize:
(w-12)(w+22)=0
W= 12
L= 12+10 = 22
Let the width of the field be w.
Then as the length of field is 10 feet more than the width, the length will be:
Length = w + 10
Area of a rectangle is given by formula:
Area = Width x Length
Substituting the above values of width and length, and the given area of the field in the above equation we get:
Area = w x (w + 10) = 264
Therefore:
w^2 + 10w = 264
Taking all the terms of the equation on left hand side we get:
w^2 + 10w - 264 = 0
To find the value of w in the above equation we factorise the expression on the left hand side as follows.
w^2 + 10w - 264
= w^2 + 22w - 12w - 264
= w(w + 22) - 12(w + 22)
= (w + 22)(w - 12)
Thus w = -22 , or 12
As width cannot be negative, w = 12
Thus:
Width of the field = 12 feet
Length of the field = Width + 10 = 12 + 10 = 22 feet.
The area of the rectangle is 264 ft^2.
The length is 10 feet more than the breadth. So one way is to examine all the factors, 2*132 , 4*66, 8*33, 8*3*11 or 24*11, 12*22 and find which of the pair of factors has the difference 10. The factors 12 and 22 fulfills thcondition. The other way is assuming l and b as lenth and breadth in feetand then,
l-b = 10 ...........(1)and
lb = 264.............(2)
So (l+b) = sqrt{(l-b)^2+4ab} = sqrt(10^2+4*264} = 34.
l-b = 10...........(1)
l+b = 34..........(3)
(1)+(3) gives: 2l = 10+34 = 44. So, l = 44/2 = 22 .
(3) - (1) gives: 2b = 34-10 = 24. So, b= 24/2 = 12.
Hope this may help.
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