The perimeter of a rectangle is 80 feet. How do you find the dimensions if the length is 5 feet longer than four times the width? What is the area of the rectangle?
Dimensions:
Area:
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To find the dimensions of the rectangle, we can set up equations based on the given information. Let's denote the width of the rectangle as ( w ) feet and the length as ( l ) feet.
Since the length is 5 feet longer than four times the width, we can write the equation for the length as: [ l = 4w + 5 ]
The formula for the perimeter of a rectangle is given by: [ \text{Perimeter} = 2(length + width) ]
Given that the perimeter is 80 feet, we can set up the equation: [ 80 = 2(l + w) ]
Now, substitute the expression for ( l ) from the first equation into the second equation: [ 80 = 2((4w + 5) + w) ]
Solve for ( w ) to find the width. Once you have the value of ( w ), you can find the length using the equation ( l = 4w + 5 ).
After finding the dimensions, you can calculate the area of the rectangle using the formula: [ \text{Area} = \text{Length} \times \text{Width} ]
Substitute the values of length and width into this formula to find the area.
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Let the width of the rectangle be ( w ) feet. The length of the rectangle is ( 5 + 4w ) feet.
The perimeter of a rectangle is given by the formula: [ P = 2 \times (\text{length} + \text{width}) ]
Given that the perimeter is 80 feet, we have: [ 80 = 2 \times ((5 + 4w) + w) ]
To find the dimensions, solve this equation for ( w ).
Once you find the value of ( w ), you can find the length of the rectangle using the expression ( 5 + 4w ).
To find the area of the rectangle, multiply the length by the width.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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