suppose the length of a rectangle increases,but the perimeter remains at 70 feet. How does the width change?
Either the width increases, decreases or remains the same. Which of these three choices makes the most intuitive sense?
We know perimeter = 2(length +width)
If perimeter = 70 then 70/2=length + width so whatever the length increases by, the width decreases by.
Thus 35 = (length + x) + (width - x)
Does that make sense?
Suppose the modified quota is 7.87
the answer that is correct for this question is that when ever the length of the rectangle increase the perimeter will stay the same and the width will decrease
No
Yes, that makes sense. If the length of the rectangle increases, but the perimeter remains the same, it means that the increase in length must be exactly balanced by a decrease in the width in order to keep the total perimeter at 70 feet. This can be understood by considering the formula for the perimeter of a rectangle, which is given by P = 2(length + width). So, if the perimeter is fixed at 70 feet, we can express this mathematically as 70 = 2(length + width). Dividing both sides of the equation by 2, we get 35 = length + width. This equation shows that the sum of the length and the width should equal 35.
Now, if the length increases by a certain value (let's call it 'x'), we can express the new length as (length + x). However, since the perimeter is unchanged, the new width must be reduced by the same value of 'x' to balance it out. Thus, the new width can be expressed as (width - x). The equation then becomes: 35 = (length + x) + (width - x).
In conclusion, if the length of a rectangle increases and the perimeter remains at 70 feet, the width must decrease by the same amount in order to maintain the balance.