The length of a rectangular field is 7 m less than 4 times the width. the perimeter is 136m ? . find the width and the length of the rectangle

➷ The perimeter is the total of all the lengths / widths

The lengths can be represented by 4x - 7

The width can be represented by x

2 times the length + 2 times the width would equal the perimeter

2(x) + 2(4x - 7) = 136

Simplify:

2x + 8x - 14 = 136

10x - 14 = 136

Add 14 to both sides:

10x = 150

Divide both sides by 10:

x = 15

The width is equal to 15m

The length is 4(15) - 7 = 53m

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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