the perimeter of a rectangle is 84 feet.The length of the rectangle is 3 feet less than 2times it width.?

Question

find the dimensions of the rectangle. Write the equation that represents this situation and will allow you to accomplish your task. Solve your equation and find the dimensions of the rectangle.

Answer 1

2 * Length + 2 * Width = Perimeter

Length = 2 * Width - 3 (from the problem)

2 * (2 * W - 3) + 2 * W = 84
4W - 6 + 2W = 84
6W = 90
W = 15ft

Length = 2 * Width - 3 (from above)
L = 2 * 15 - 3
L = 30 -3
L = 27ft

Check the Answer:
2 * 15 + 2 * 27 = 84
30 + 54 = 84
84 = 84 Check!

Answer 2

perimeter = the sum of the sides

a rectangle has two pairs of equal sides
that is, two lengths and two widths

let ...........L = length ..............and ...................... W = width

then ..............Perimeter = L + L + W + W

.............. P ... = 2L + 2W ..............where P is the perimeter

This is the basic perimeter formula you need to start with

NOW.....
what info were you given ...

.... P = 84

.......... and .................the length is 3 less than 2 times the width

which in math symbols is

....................................... L = 2W - 3

substituting this value for the length in the perimeter formula gives

..................... P = 2L + 2W

............... = 2( 2W - 3) + 2W .................... expand and simplify

...............= 4W - 6 + 2W

.............. = 6W - 6 .................................. so

.......... P = 6W - 6 ...... but you were also given that P= 84

so ... you have an expression for P ..... P= 6W - 6
and a value expression for P .. ....P = 84

putting them equal to each other gives you an expression in one variable only ( W ) that you can then solve ie.,

P = 6W =- 6 = 84 ie.,

6W - 6 =84 solving, gives

6W = 84 + 6 adding 6 to both sides

6W = 90
now solve for W ,
by dividing both sides by 6

W = 90 / 6 = 15 (ninety divided by six)

thus , W = width = 15

and from the earlier expression for length

L = 2W - 3 now substitute W = 15, to give

L = 2(15) - 3

L = 30 - 3

L = 27

Summarizing, you have

W = 15 and

L = 27

but are these the correct values ?

put them into the original basic expression for the perimeter and see what you get .......

P = 2L +2W

P = 2(27) + 2(15)

P = 54 + 30

P = 84 hurray it works

So there you have it

the width is 15 ft and
the length is 27 ft
which as you saw above means that the P is 84 ft.............

ALSO note that the length is 3 less than twice the width , since
2W = 2(15) = 30

and 2w - 3 = 30 - 3 = 27 =L

hope that helped

good luck

Answer 3

Okay... to get the perimeter of a rectangle, you add the lengths of the 4 sides together. You've got 2 pairs of lines, so lets say that 2X + 2Y = perimeter of rectangle.

If the length of the rectangle is X and the width is Y, then according to your problem, X=2Y-3.

So if 2X + 2Y = 84, and X= 2Y-3, then you substitute 2Y-3 wherever there is an X:

2(2Y-3) + 2Y = 84 then multiply it out...
4Y - 6 + 2Y = 84 then add the Ys together...
6Y - 6 = 84 then add 6 to both sides...
6Y=90 then divide both sides by 6...
Y=15. Then you go back and substitute 15 in the X=2Y-3...
X=2(15)-3 then do the math...
X=30-3 and
X=27.

So if X =27 and Y=15, check to make sure that it's right by adding for the perimeter... 27+27+15+15=84.

In a mathematical word problem, "is" always can be substituted by an = sign. Hope this helps, and good luck with the rest of your homework!

Answer 4

the equation for perimeter of all quadrilaterals (including a rectangle) is P = 2*W + 2*L. it is given that the length is 3 feet less than 2 times its width, so L = 2*W - 3. you now have two variables solved: P = 84 feet (given in the question), and L= 2*W - 3. using substitution, add these equations to the perimeter equation:

P = 2*W + 2*L
L = 2*W - 3
P = 84 feet

substitute P in P=2*W + 2*L with 84 feet, so

84 ft = 2*W + 2*L

now, substitute L in that equation with 2*W - 3. you get

84 ft = 2*W + 2*(2*W - 3)
(by the way, this is the equation that represents the situation)

now, just solve through basic laws of equality.

84 ft = 2W + 2(2W-3)
84 ft = 2W + 4W - 6 (distribution)
(84 + 6) ft = 2W + 4W - 6 + 6 (addition)
90 ft = 6W (simplification)
90/6 ft = 6W/6 (division)
15 ft = W (simplification)

use L=2*W-3 to find the length:

L = 2*(15 ft) - 3
L = 30 ft - 3
L = 27 ft

Answer 5

enable x = the width enable 3x-9 = the size Perimeter = 2L+2W Perimeter = 2(3x-9) + 2x resolve for x 6x-18+2x=206 8x-18=206 8x=224 x=28 The length subsequently could be 3(28)-9 = seventy 5 and the width could be 28.

Answer 6

P=84ft
L=2W-3

P=2W+2L
2w+2(2w-3)=84
2w+4w-6=84
6w=90
w=15
l=27

Answer 7

let the length = l and the width = w

84= 2l + 2w

the length = 2w-3

84 = 2(2w-3) + 2w
84 = 4w - 6 + 2w
84 = 6w - 6
90 = 6w
15 = w
l = 2w-3
l = 2(15)-3
l = 27

Answer 8

L = Length
W = Width
L = 2W - 3
2L + 2W = 84
2.(2W - 3) + 2W = 84
4W - 6 + 2W = 84
6W = 90
W = 15 ft
L = 30 - 3
L = 27ft
Dimensions are 15 ft by 27 ft

Answer 9

84=2W + 2(2W - 3)
84=2W + 4W - 6
84=6W - 6
90=6W
15=W

L= (2 x 15) - 3
L= 30 - 3
L=27

To Check... 27 + 27 + 15 + 15 = 84

Answer 10

2l + 2w = 84
l = 2w-3
2(2w-3) +2w = 84
4w-6 +2w = 84
6w = 90
w = 15
l = 2(15) -3
l = 27
Length = 27 feet, width = 15 feet