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?

Answer 1

Dimensions: #33 xx 7# feet
Area: #231# square feet

Assigning the variables #L# for length and #W# for width. (unless otherwise noted all values are in "feet")
We are told that the perimeter is #80# feet; since the perimeter of a rectangle is 2 times the length plus the width: #color(white)("XXX")2(L+W)=80# #color(white)("XXXXX")rarr L+W=40# #color(white)("XXXXX")rarr L=40-W#
We are also told that the length is 5 feet longer than four times the width: #color(white)("XXX")L=4W+5#
Combining these two we have: #color(white)("XXX")4W+5=40-W# #color(white)("XXXXX")rarr 5W=35# #color(white)("XXXXX")rarr W=7#
Re-using the earlier equation: #L=40-W#, we get: #color(white)("XXX")L=40-7=33#
Since the area of a rectangle is equal to the length times the width: #color(white)("XXX")"Area"_square =33 xx 7 = 231 #(square feet)
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Answer 2

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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Answer 3

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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Answer from HIX Tutor

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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