the perimeter of a rectangle is 70 feet. the length and width are the ratio 3 and 2. find the length and width.
2006-06-18 15:16:23 · 18 answers · asked by koalabear 2 in Science & Mathematics ➔ Mathematics
3x+3x+2x+2x=70
10X=70
x= 70/10
X=7
3*7=21
2*7=14
the length and width are 21,14
2006-06-18 15:24:17 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Length= 21 feet & width = 14 feet
Verification: Perimeter of a rectangle = 2 (l+w)
= 2 (21+14)
= 70 feet
2006-06-24 22:33:58 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Since the ratio of length to width is 3 to 2, let x be a constant such that 2x + 2x + 3x + 3x = 70 sets up the equation. Then 10x = 70 or x = 7. This means width is 2 * 7 = 14 and length is 3 * 7 = 21. Now check: 2 * 14 + 2 * 21 = 28 + 42 = 70.
2006-06-18 22:34:37 · answer #3 · answered by flyfisher_20750 3 · 0⤊ 0⤋
1. a rectangle is a 4 sided object
2. the sides of a rectangle that are on opposite sides of one another are equal in length.
3. the perimeter of an object is equal to the total length of all sides added together..
In your problem the sides have a ratio of 3:2 -- so let's just assume that the rectangle's length=3*X and the width=2*x....
The perimeter of this object would be 2*length + 2*width.
Replacing with the values above... 2*3X + 2*2X = perimeter
Set this equation equal to '70 feet' as given in your word problem and calculate what 'X' is equal to... 6X+4X=10X=70 ft.
X = 7 ft.
Now to figure out the length and width of your rectangle plug X into the equations for length and width.. length = 3X = 3(7ft) = ?? ft and width = 2X = 2(7ft) = ?? ft.
2006-06-18 22:33:07 · answer #4 · answered by hallibur 1 · 0⤊ 0⤋
add the two numbers in the ratio, to get 5. Then, devide 70 by 5, to get 14, but you must divide that in half because P=2(l+w)
you should get 7 after dividing. Then multiply 7 by each of the ratio numbers, and you get a length and width of 21 and 14.
Hope this helps!
2006-06-19 10:54:36 · answer #5 · answered by quickster94 3 · 0⤊ 0⤋
let L=length and W=width
Perimeter=2L + 2W
Ratio: 3:2, 3 W for every 2 L
2L:3W
2L=3W
L=3W/2
therefore: P=2(L + W)
70=2(3/2 W + W)
70=2(3/2 W + 2/2 W)
70=2(5/2 W)
Cross multiply:
70/5= W
14=W
since L=3W/2
L=3 x 14/2
L=21
Therefore: Length = 21 feet and Width is 14 feet
Checking: P=2(21+14)
P=70
2006-06-18 22:41:46 · answer #6 · answered by alexander c 1 · 0⤊ 0⤋
14 W and 21 H
14 + 14 + 21 + 21 = 70
2006-06-18 22:26:06 · answer #7 · answered by hththted 3 · 0⤊ 0⤋
Its 14 x 21
2006-06-18 22:22:39 · answer #8 · answered by compagent 1 · 0⤊ 0⤋
perimeter (P) = 2W + 2L = 70 ft
Since the given ratio: L/W = 3/2 --> L = (3/2)*W <--> substitute this into the first equation to find W =14.
--> L=(3/2)*W = (3/2)*14 = 21
Hope that helps.
2006-06-18 22:29:45 · answer #9 · answered by chd.tran 2 · 0⤊ 0⤋
The lenght is 21 ft and width is 14 feet
2006-06-18 22:25:39 · answer #10 · answered by Deborah O 1 · 0⤊ 0⤋
L= 3X
W=2X
According to Question,
2(L+W)= Perimeter
2(3x+2x)=70
5x=35
x=7
therefore
L= 3*7=21
W=2*7=14
2006-06-19 00:09:15 · answer #11 · answered by thegame1 1 · 0⤊ 0⤋