2007-10-02 05:42:41 · 8 answers · asked by bayleycs 1 in Science & Mathematics ➔ Mathematics
The area of a rectangle is length x width, or
a = l * w (that's a lower case L)
You also know that l = w +9. Substitute:
a = (w + 9) * w = 1620
w^2 + 9w - 1620 = 0
Use the quadratic formula, and get
w = 36 or w = -45
Ignore the meaningless negative result, so w = 36 and thus your answer is l = 45.
2007-10-02 06:00:01 · answer #1 · answered by coryfucius 3 · 0⤊ 0⤋
Area formula
A = LW
let
w = width
w + 9 = length
1620 = square yards
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The equation
1620 = (w + 9)w
1620 = w² + 9w
Transpose 1620
1620 - 1620 = w² + 9w - 1620
Collect like terms
0 = w² + 9w - 1620
The first term w² = 1
The middle term is + 9w
Find the sum of the middle term
Multiply the first term 1 times the last term 1620 equals 1620 and factor
Factors of 1620
1 x 1620
2 x 810
3 x -540
4 x 405
5 x 324
5 x 324
6 x 270
9 x 180
10 x 162
12 x 135
15 x 108
18 x 90
20 x 81
27 x 60
30 x 54
36 x 45. . .←. .use the factors
+ 45 and - 36 satisfy the sum of the middle term
Insert + 45w and - 36w into the equation
0 = w² + 9w - 1620
0 = w² + 345w - 36w - 1620
Group factor
0 = (w² + 45w) - (36w - 1620)
0 = [w(w + 45) - 36(w + 45)]
0 = (w - 36)(w + 45)
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Roots
w - 36 = 0
Transpose 36
w - 36 + 36 = 0 + 36
w = 36. . .←. .The width
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Roots
w + 45 = 0
Transpose 45
w + 45 - 45 = 0 - 45
w = - 45. . ← . .not used
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The width is 36 yards
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The length is w + 9
36 + 9 = 45
The lengh is 45 yards
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2007-10-02 08:03:57 · answer #2 · answered by SAMUEL D 7 · 0⤊ 0⤋
The formula you need is 2l x 2w=P okay so you know that the length is 9 yards longer than the width. So to put this into a problem you would do:
2(9+w) x 2w = 1620 because the lenght is 9 longer than the width you write it as 9+w because you are going to take whatever you get for the width and add 9 to it.
so then distribute. 18 + 2w x 2w = 1620 then add like terms
18 + 4w = 1620 you are going to want to move the 18 to the other side so you minus 18 from 1620 it might look something like this
18+ -18 + 4w = 1620 -18 I added the negative 18 to show how you would get rid of it
4w =1602 now you need to get w alone so you would take 4 and put a 1 under it like 4/1 then you would do the inverse of 4/1 which would be 1/4. You take 1/4 and move it to the other side. You also need to put a 1 under the 1602 it should look like this.
w= 1602/1 divided by 1/4 which would equal 400.5 then add 9 to the width so the length is 409.5
L= 409.5
w= 400.5
To check your work take the lenght which is 409.5 times 2 and you get 819
Then take the width 400.5 times 2 and you get 801
Then add 819 + 801 and you get 1620.
Hope this helped you understand.
2007-10-02 06:47:08 · answer #3 · answered by christin k 2 · 0⤊ 0⤋
A=lw
l=w+9
A=w(w+9)
A= 1620
w(w+9)=1620
w^2+9w+1620
w^2 + 9w-1620=0
using quadratic formula, w=36 and -45. and you can't have a negative length so the width is 36 and the length is 36+9 which is 45.
2007-10-02 06:01:37 · answer #4 · answered by Nilly 3 · 0⤊ 0⤋
Perimeter of square = perimeter of rectangle 4 (52.5 mm) = 2 (25 mm) + 2(W) W is the variable we wish to solve for. 210 = 50 + 2(W) 160 = 2(W) 80 = W Note the cm in the square's length and the conversion. The width is 80 mm
2016-05-19 05:49:54 · answer #5 · answered by ? 3 · 0⤊ 0⤋
Let length=l
width=w
area=lw=1620
l=w+9
(w+9)w=1620
w^2+9w-1620=0
solving w=36 OR -45
WIDTH=36 (CAN'T BE NEGATIVE)
length=45
2007-10-02 06:04:12 · answer #6 · answered by cidyah 7 · 0⤊ 0⤋
width(width + 9) = 1,620
width^2 + 9width = 1,620
width^2 + 9 width - 1620 = 0
(width + 45)(width - 36) = 0
width + 45 = 0, width = - 45
width - 36 = 0, width = 36
Answer: the length is 45 (36 + 9) feet.
Proof (area is 1,620 square feet):
= 45 feet * 36 feet
= 1,620 square feet
2007-10-05 22:46:06 · answer #7 · answered by Jun Agruda 7 · 2⤊ 0⤋
(L-9)xL=1620
L²-9L=1620
L²-9L-1620=0
Apply the quadratic formula
L=45
45 x 36 = 1620
45 - 9 = 36
2007-10-02 05:51:54 · answer #8 · answered by PoppaJ 5 · 1⤊ 0⤋