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.
