The width of a rectangle is 6 in. less than its length. The perimeter is 68 in.
What is the width of the rectangle?
(not multiple choice) my answer is 14
5(a-4) - 8a = 55 (not multiple choice) my answer -25
2n-7/3 = 15 (not multiple choice) my answer is 6
first one correct.
Multiply both sides by 3.
6n - 7 = 45
Add 7 to both sides.
6n = 52
Divide by 6.
To find the width of the rectangle, we can set up an equation based on the given information.
Let's assign the length of the rectangle as 'l' and the width as 'w'.
We are given that the width is 6 inches less than its length, so we can write the equation:
w = l - 6
The perimeter of a rectangle can be calculated using the formula:
perimeter = 2(l + w)
Given that the perimeter is 68 inches, we can substitute the values:
68 = 2(l + w)
Next, we can substitute the value of 'w' from the first equation into the second equation:
68 = 2(l + (l - 6))
Now, simplify the equation:
68 = 2(2l - 6)
68 = 4l - 12
Add 12 to both sides:
68 + 12 = 4l - 12 + 12
80 = 4l
Divide both sides by 4:
80/4 = 4l/4
20 = l
So, the length of the rectangle is 20 inches.
Now, substitute the value of 'l' into the first equation to find the width:
w = 20 - 6
w = 14
Therefore, the width of the rectangle is 14 inches.
For the equation 5(a - 4) - 8a = 55:
To solve for 'a', start by distributing the 5 to the terms inside the parentheses:
5a - 20 - 8a = 55
Combine like terms on the left side:
-3a - 20 = 55
Add 20 to both sides:
-3a - 20 + 20 = 55 + 20
-3a = 75
Divide both sides by -3:
-3a/-3 = 75/-3
a = -25
Therefore, the value of 'a' is -25.
For the equation 2n - 7/3 = 15:
To solve for 'n', start by multiplying both sides of the equation by 3 to get rid of the fraction:
3 * (2n - 7/3) = 3 * 15
6n - 7 = 45
Now, add 7 to both sides:
6n - 7 + 7 = 45 + 7
6n = 52
Divide both sides by 6:
6n/6 = 52/6
n = 8.67
Therefore, the value of 'n' is approximately 8.67 (rounded to two decimal places).
To find the width of the rectangle, we need to set up an equation using the given information.
Let's say the length of the rectangle is L. According to the problem, the width is 6 inches less than the length, so the width would be L - 6.
The formula for finding the perimeter of a rectangle is: Perimeter = 2(length + width)
Given that the perimeter is 68 inches, we can substitute the values into the equation:
68 = 2(L + (L - 6))
Simplifying the equation:
68 = 2(2L - 6)
Divide both sides by 2:
34 = 2L - 6
Add 6 to both sides:
34 + 6 = 2L
40 = 2L
Divide both sides by 2:
20 = L
Therefore, the length of the rectangle is 20 inches.
Now, we can find the width by subtracting 6 inches from the length:
Width = 20 - 6 = 14 inches.
So, the width of the rectangle is 14 inches.
Regarding the equation 5(a-4) - 8a = 55, to solve for the value of a, we can follow these steps:
1. Distribute 5 into the parentheses: 5a - 20 - 8a = 55.
2. Combine like terms by subtracting 8a from 5a: -3a - 20 = 55.
3. Add 20 to both sides to isolate the variable: -3a = 75.
4. Divide both sides by -3: a = -25.
Hence, the value of a is -25.
Lastly, for the equation 2n - 7/3 = 15, we can follow these steps to solve for n:
1. Multiply both sides by 3 to eliminate the fraction: 3(2n - 7/3) = 3(15).
2. Distribute 3 into the parentheses: 6n - 7 = 45.
3. Add 7 to both sides to isolate the variable: 6n = 52.
4. Divide both sides by 6: n = 52/6 = 26/3.
Therefore, the value of n is 26/3, which can also be expressed as 8 and 2/3.