The perimeter of a rectangular carpet is 70feet. The with is three -fourths the length .Find the width.

38.
The length of a rectagular room is six times as the width . The perimeter 84 yards. find the width.

39.
The width of a rectangle is 12 less than the length. The perimeter is 108 units Finf the length.

P= 2L + 2W= 2L + 2(3/4 L)

solve for L, you know Perimeter. Then, width is 3/4 L

2) P= 2L + 2W= 2*6W + 2W
solve for W

L = 84/12 = 7

W = 7/4 = 1.75

3) P= 2L + 2W= 2L + 2(L-12)
solve for L, you know Perimeter. Then, width is L-12

L = 108/4 = 27
W = 27-12 = 15

To solve question 38, we are given that the perimeter of a rectangular carpet is 70 feet. We are also told that the width is three-fourths the length.

Let's denote the length as L and the width as W.

The formula for the perimeter of a rectangle is P = 2L + 2W.

Substituting the given information, we can write the equation as follows:
70 = 2L + 2(3/4L)

To simplify, we multiply the 2 by the 3/4L:
70 = 2L + (6/4)L

Combining like terms, we have:
70 = (8/4)L + (6/4)L

Combining the fractions and simplifying further, we get:
70 = (14/4)L

To isolate L, we multiply both sides of the equation by 4/14:
(4/14)*70 = L

Simplifying further, we find that:
L = 20

Now that we have the length, we can find the width by considering that it is three-fourths the length:
W = (3/4)L
W = (3/4)*20
W = 15

Therefore, the width of the rectangular carpet is 15 feet.

To solve question 39, we are given that the length of a rectangular room is six times the width. The perimeter of the room is 84 yards.

Let's denote the width of the room as W.

The formula for the perimeter of a rectangle is P = 2L + 2W.

Substituting the given information, we can write the equation as follows:
84 = 2(6W) + 2W

Simplifying the equation, we get:
84 = 12W + 2W

Combining like terms, we have:
84 = 14W

To isolate W, we divide both sides of the equation by 14:
84/14 = W

Simplifying, we find that:
W = 6

Therefore, the width of the rectangular room is 6 yards.

To solve the first question, we are given the perimeter of a rectangular carpet, which is 70 feet. We are also told that the width is three-fourths the length.

To find the width, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

In this case, we have P = 70 feet and W = (3/4)L. Substituting these values into the formula, we get:

70 = 2L + 2(3/4)L

To simplify the equation, we can multiply 2 by (3/4) which gives us (6/4). Therefore, the equation becomes:

70 = (8/4)L + (6/4)L

Combining the like terms on the right side, we get:

70 = (14/4)L

To isolate L, we can multiply both sides of the equation by the reciprocal of (14/4), which is (4/14):

(4/14) * 70 = (4/14) * (14/4)L

Simplifying the left side, we have:

20 = L

Therefore, the length of the rectangular carpet is 20 feet.

To find the width, we can substitute the value of L back into the expression for the width:

W = (3/4)L

W = (3/4)*20

Simplifying the expression, we get:

W = 15

Therefore, the width of the rectangular carpet is 15 feet.

For the second question, we are given the perimeter of a rectangular room, which is 84 yards. We also know that the length of the room is six times the width.

Using the same formula for the perimeter of a rectangle, which is P = 2L + 2W, we can set up the equation:

84 = 2L + 2W

Since we are given that the length of the room is six times the width, we can write L = 6W. Substituting this into the equation, we get:

84 = 2(6W) + 2W

Simplifying, we have:

84 = 12W + 2W

Combining like terms on the right side, we get:

84 = 14W

To isolate W, we can divide both sides of the equation by 14:

(1/14) * 84 = (1/14) * 14W

Simplifying, we have:

6 = W

Therefore, the width of the rectangular room is 6 yards.

For the third question, we are given the perimeter of a rectangle, which is 108 units. We are also told that the width of the rectangle is 12 less than the length.

Using the formula for the perimeter of a rectangle, which is P = 2L + 2W, we can set up the equation:

108 = 2L + 2W

Since we are given that the width is 12 less than the length, we can write W = L - 12. Substituting this into the equation, we get:

108 = 2L + 2(L - 12)

Simplifying, we have:

108 = 2L + 2L - 24

Combining like terms on the right side, we get:

108 = 4L - 24

To isolate L, we can add 24 to both sides of the equation:

108 + 24 = 4L

Simplifying, we have:

132 = 4L

To find the value of L, we can divide both sides of the equation by 4:

(1/4) * 132 = (1/4) * 4L

Simplifying, we get:

33 = L

Therefore, the length of the rectangle is 33 units.