The perimeter of a rectangle is 70 cm. The width is (4x - 1)cm and the length is (6x - 4)cm. What is the length of the rectangle?
2007-02-04 06:05:12 · 13 answers · asked by freya 1 in Science & Mathematics ➔ Mathematics
l= 20 cm
multiply the equations for width and legnth by 2 then set that equal to 70 cm to solve for x
then plug that vaulue into the equation for legnth
2007-02-04 06:09:11 · answer #1 · answered by Billy K 3 · 0⤊ 0⤋
The formula for the perimeter of a rectangle is
P = 2L + 2W.
We have P (it's 70), the length (which is 6x - 4) and the width (which is 4x - 1). Therefore
70 = 2(6x - 4) + 2(4x - 1)
Expand the right hand side,
70 = 12x - 8 + 8x - 2
70 = 20x - 10
80 = 20x; therefore
x = 4
Now that we have the value of x, we can determine the length.
Since L = 6x - 4 and x = 4, then
L = 6(4) - 4 = 24 - 4 = 20
So the length is 20 cm
2007-02-04 06:10:22 · answer #2 · answered by Puggy 7 · 0⤊ 0⤋
To answer this question, keep in mind that the perimiter is twice the width plus twice the length. So, 70 = 2(4x-1) + 2(6x-4).
70 = 2(4x-1) + 2(6x-4) divide everything by 2
35 = 4x - 1 + 6x - 4 combine like terms
35 = 10x - 5 add 5 to both sides
40 = 10x divide both sides by 10
4 = x you have solved for x
Now, simply substitute 4 for x in the equation for the length.
length = 6x - 4 substitute 4 for x
length = 6(4) - 4 multiply
length = 24 - 4 subtract
length = 20 cm final answer
Hope this helps!
2007-02-04 06:13:50 · answer #3 · answered by Penya 4 · 0⤊ 0⤋
Perimeter Formula
P = 2L + 2W
70 = 2(6x - 4) + 2(4x - 1)
70 = 12x - 8 + 8x - 2
70 = 20x - 10
70 + 10 = 20x - 10 + 10
80 = 20x
80/20 = 20x/20
4 = x
The answer is x = 4
Insert the x value into the equation
- - - - - - - - - - - - - - - - - - - - - --
P = 2L + 2w
70 = 2(6x - 4) + 2(4x - 1)
70 = 2[6(4) - 4] + 2[4(4) - 1]
70 = 2[24 - 4] + 2[16 - 1]
70 - 2[20] + 2[15]
70 = 40 + 30
70 = 70
- - - - - - - - -
The length is 6x - 4
6(4) - 4 =
24 - 4
20
The length is 20 cm for one side.
- - - - - - - - - -s-
2007-02-04 07:11:01 · answer #4 · answered by SAMUEL D 7 · 0⤊ 0⤋
this is a fun one. Ok perimeter of a rectangle is 2w + 2l right?
so... 2(4x-1) + 2(6x-4) = 70cm
simplify to 20x -10 = 70cm
and solve for x to find that x = 4 cm we aren't done though
plug that into the length formula to get the length equal to 20 cm.
2007-02-04 06:11:38 · answer #5 · answered by gwalman 2 · 0⤊ 0⤋
P = perimeter
W = width
L = length
P=2L + 2W
Now, plug in what you know.
70 = 2(6x-4) + 2(4x -1)
Then, solve for x.
70 = 12x - 8 + 8x - 2
70 = 20x - 10
7 = 2x - 1
8 = 2x
x = 4
Then, plug in 4 for x in the length.
L = 6x - 4
L = 6(4) - 4
L = 24-4
L = 20
Don't forget the units!
L = 20 cm
The length is 20 cm.
2007-02-04 06:19:27 · answer #6 · answered by yankees921 1 · 0⤊ 0⤋
2(4x-1)+2(6x-4)=70
there are 2 lengths and widths
8x-2+12x-8=70
distribute the 2
20x-10=70
do algebra
20x=80
more algebra
x=4
blah blah bah
length=20
plug x into the length and wah lah!
2007-02-04 06:12:10 · answer #7 · answered by Anonymous · 0⤊ 0⤋
70 = 2[4x - 1] + 2[6x - 4]
70 = 2x - 2 + 12x - 8
70 = 14x - 10
80 = 14x
40/7 = x
so width = 4(40/7) - 1 = 160/7 - 7/7 = 153/7
and length = 6(40/7) - 4 = 240/7 - 28/7 = 212/7
2007-02-04 06:11:12 · answer #8 · answered by Philo 7 · 0⤊ 0⤋
P =2(w+l)
70 = 2(4x-1+6x-4)
35 = 10x-5
40 = 10x
x= 4
6(4) - 4 = 20cm
2007-02-04 06:09:35 · answer #9 · answered by 7 · 0⤊ 0⤋
per = 2(l+w)
70 = 2 ({6x-4} + {4x-1})
70/2 = {6x-4} + {4x-1}
35 = 6x - 4 + 4x - 1
35 + 4 + 1 = 6x + 4x
40 = 10x
40/10 = x
4 = x
then substitute 4 in 6x-4
l = 6(4) - 4
= 20cm
2007-02-04 06:18:05 · answer #10 · answered by Sarah 1 · 0⤊ 0⤋