To have a different rectangle with the same perimeter you just have different measurements. If you need an example let me know!
Answer:
4,600
Step-by-step explanation:
1,200+1,200+1,100+1,100
Answer:
Step-by-step explanation:
Hello, please consider the following.

So this is divisible by 3.
Now, to prove that this is divisible by 9 = 3*3 we need to prove that
is divisible by 3. We will prove it by induction.
Step 1 - for n = 1
4+17=21= 3*7 this is true
Step 2 - we assume this is true for k so
is divisible by 3
and we check what happens for k+1

is divisible by 3 and
is divisible by 3, by induction hypothesis
So, the sum is divisible by 3.
Step 3 - Conclusion
We just prove that
is divisible by 3 for all positive integers n.
Thanks
Given Information:
Area of rectangle = 16 square feet
Required Information:
Least amount of material = ?
Answer:
x = 4 ft and y = 4 ft
Step-by-step explanation:
We know that a rectangle has area = xy and perimeter = 2x + 2y
We want to use least amount of material to design the sandbox which means we want to minimize the perimeter which can be done by taking the derivative of perimeter and then setting it equal to 0.
So we have
xy = 16
y = 16/x
p = 2x + 2y
put the value of y into the equation of perimeter
p = 2x + 2(16/x)
p = 2x + 32/x
Take derivative with respect to x
d/dt (2x + 32/x)
2 - 32/x²
set the derivative equal to zero to minimize the perimeter
2 - 32/x² = 0
32/x² = 2
x² = 32/2
x² = 16
x =
ft
put the value of x into equation xy = 16
(4)y = 16
y = 16/4
y = 4 ft
So the dimensions are x = 4 ft and y = 4 ft in order to use least amount of material.
Verification:
xy = 16
4*4 = 16
16 = 16 (satisfied)
65 feet squared.
8 times 10 is eighty, then you need to subtract 3 time 5 (which is 15), and that makes it 65 feet squared.