The width of a rectangle is two-thrid of the length.if the perimeter is 192,find the width.
Perimeter = 2L + 2W
192 = 2L + 2W
W = 2/3 L
192 = 2L + 2 (2/3)L
192 = 2L + 4/3 L
192 = 6/3 L + 4/3 L
192 = 10/3 L
Multiply each side by 3/10 to find the Length then substitute that answer into the original equation to find the width.
To find the width of the rectangle, we need to know the length of the rectangle. However, the given information about the perimeter can help us solve for the length.
Let's say the length of the rectangle is "L".
According to the given information, the width is two-thirds of the length, which means the width is (2/3)L.
The formula for the perimeter of a rectangle is 2(length + width). Plugging in the given perimeter of 192, we can set up the equation:
2(L + (2/3)L) = 192
Multiplying 2 to both terms inside the brackets:
2L + (4/3)L = 192
Combining like terms:
(6/3)L + (4/3)L = 192
Simplifying the left side:
(10/3)L = 192
To isolate L, we can multiply both sides by the reciprocal of (10/3), which is (3/10):
L = (192 * 3) / 10
L = 576 / 10
L = 57.6
Now that we have the length, we can find the width by substituting the length back into the original expression for the width:
Width = (2/3) * 57.6
Width = 38.4
Therefore, the width of the rectangle is 38.4.
To find the width of a rectangle, given that the width is two-thirds of the length and the perimeter is 192, we can follow these steps:
Step 1: Assign variables:
Let's assign 'w' as the width and 'l' as the length of the rectangle.
Step 2: Set up the equations:
Based on the given information, we can set up two equations:
- The width is two-thirds of the length: w = (2/3)l
- The perimeter is given by the formula: perimeter = 2(w + l)
Step 3: Substitute the width equation into the perimeter equation:
Substituting w = (2/3)l into the perimeter equation, we get:
192 = 2((2/3)l + l)
Step 4: Simplify and solve for l:
Simplifying the equation, we have:
192 = 2(5/3)l
Dividing both sides by 2, we get:
96 = (5/3)l
To isolate l, we multiply both sides by 3/5:
(3/5) * 96 = l
57.6 = l
Therefore, the length of the rectangle is 57.6.
Step 5: Calculate the width:
Substituting the value of the length (l = 57.6) into the width equation:
w = (2/3) * 57.6
w = 38.4
So, the width of the rectangle is 38.4.