Question

The width of a rectangle is 2 cm less than 8 times the length. The perimeter is 68 cm. What are the width and length of the rectangle?

Answer 1

Answer:

length=4

width=30

Step-by-step explanation:

length=x

width=8x-2

(8x-2)*2+2x=68

16x-4+2x=68

18x=72

x=4 (Length)

4*8=32, 32-2=30(width)

Answer 2

Answer:

length=4 cm

Width=30 cm

Step-by-step explanation:

Hello, I am glad I can help you with this.

Step one

define the equations

the perimeter of a rectangle is given by:

Perimeter=2*length+2*width

Let

Perimeter (P)

length(L)

Width(W)

P=2L+2W

68=2L+2W,equation (1)

The width of a rectangle is 2 cm less than 8 times the length, in other words, you can take the width and add 2 cm to find 8 times the length,in mathematical terms it is

W+2=8L, isolating W

W=8L-2,equation (2)

Step two

use equation (1) and equation (2) to find L and W

replace W from equation (2) into equation (1)

68=2L+2(8L-2)

68=2L+16L-4

68=18L-4

isolating L

68+4=18L

72/18=L

L=4 cm

replace the value of L in equation (2)

W=8L-2

W=8(4 )-2

W=32-2

W=30 cm

Hence,

length=4 cm

Width=30 cm

Have a good day.