the length of a rectangle is 9 centimeters more than half the width . Find the length if the perimeter is 60cm.
I know the answer is 16 cm, but I got a different answer. please help
width = w
length = w/2 + 9
30 = half perimeter = w + w/2 + 9
21 = 3 w /2
w = 42/3
length = w/2 + 9 = 42/6 + 9
=7+9 = 16 sure enough
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To solve this problem, we'll first set up some equations based on the given information.
Let's start by assuming the width of the rectangle is "w" centimeters. According to the problem, the length is 9 centimeters more than half the width, which can be represented as (w/2) + 9.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the perimeter is given as 60 cm. So, we can set up the equation:
60 = 2((w/2) + 9 + w)
Now, let's simplify the equation step by step:
60 = 2(w/2 + 9 + w)
60 = w + 18 + 2w
60 = 3w + 18
42 = 3w
w = 14
So, we have found that the width of the rectangle is 14 centimeters.
Now, we can find the length by substituting the value of width into the expression we found earlier: l = (w/2) + 9.
l = (14/2) + 9 = 7+9 = 16
Therefore, the length of the rectangle is 16 centimeters.
If you obtained a different answer, please double-check your calculations to make sure you didn't make any errors while solving the equation.
To solve this problem, let's introduce variables:
Let's assume that the width of the rectangle is "w" cm.
According to the question, the length of the rectangle is 9 centimeters more than half the width, which can be written as: (1/2)w + 9 cm.
The formula for the perimeter of a rectangle is given by: P = 2(length + width).
Substituting the given values, we have:
60 cm = 2((1/2)w + 9 cm + w)
Simplifying, we get:
60 cm = 2(w/2 + 9 cm + w)
60 cm = (w + 18 cm + 2w)
60 cm = 3w + 18 cm
Next, we need to solve for the value of "w" by isolating it on one side of the equation:
Subtracting 18 cm from both sides, we have:
60 cm - 18 cm = 3w
42 cm = 3w
Dividing both sides of the equation by 3, we get:
42 cm / 3 = w
14 cm = w
So, the width of the rectangle is 14 cm.
To find the length, we need to substitute this value back into our earlier expression for the length:
Length = (1/2)w + 9 cm
Length = (1/2)(14 cm) + 9 cm
Length = 7 cm + 9 cm
Length = 16 cm
Therefore, the length of the rectangle is 16 cm.