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.