1. The perimeter of a rectangle is 78 cm. The length is 3 greater than twice its width. Find the dimensions.
Let's start by representing the width of the rectangle as "w" cm.
According to the problem, the length of the rectangle is 3 greater than twice its width. So we can represent the length as "2w + 3" cm.
The formula for calculating the perimeter of a rectangle is:
Perimeter = 2(length + width)
Given that the perimeter is 78 cm, we can substitute the values into the formula:
78 = 2((2w + 3) + w)
Simplifying the equation:
78 = 2(3w + 3)
78 = 6w + 6
Now, let's isolate the variable "w":
6w = 78 - 6
6w = 72
Dividing both sides by 6:
w = 72/6
w = 12
Now that we have the value of "w," we can find the value of the length:
Length = 2w + 3
Length = 2(12) + 3
Length = 24 + 3
Length = 27
So, the dimensions of the rectangle are:
Width = 12 cm
Length = 27 cm
To find the dimensions of the rectangle, we'll use the given information about its perimeter and the relationship between its length and width.
Let's assume the width of the rectangle is "w" cm. According to the given information, the length of the rectangle is 3 more than twice its width. So, the length can be represented as "2w + 3" cm.
Now, we can calculate the perimeter of the rectangle using the formula: Perimeter = 2(length + width).
Given that the perimeter is 78 cm, we can substitute the values of length and width into the formula and solve for w:
78 = 2(2w + 3 + w)
78 = 2(3w + 3)
78 = 6w + 6
78 - 6 = 6w
72 = 6w
w = 12
Therefore, the width of the rectangle is 12 cm. To find the length, we substitute this value back into the expression for length:
length = 2w + 3 = 2(12) + 3 = 24 + 3 = 27 cm
Thus, the dimensions of the rectangle are width = 12 cm and length = 27 cm.
wtf is the answer
78 = 2(2w + 3) + 2w
78 = 6w + 6
72 = 6w
? = w