a rectangle has a perimeter of 22 feet. the width is 5 feet less than the length. find the length and width of the rectangle

the length is 8ft

the width is 3ft

Step-by-step explanation:

Step one:

given

perimter= 22ft

let the length be x

width = x-5

Step two

the expression for the perimeter of a rectangle is

P=2L+2W

substituting our data

22= 2(x)+2(x-5)

open brackets

22=2x+2x-10

collect terms and solve for x

22+10=4x

32=4x

divide both sides by 4

x= 32/4

x= 8ft

the length is 8ft

the width = x-5= 8-5= 3ft

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt