We know the perimeter is the sum of all sides. So lenght+length+width+width = 2length+2width.
Let's call the width x. If the length is 4m longer, then it's x+4.
We know the perimeter, so we can make an equation:
56=2x+2(x+4)
And solve from there:
56=2x+2x+8
56=4x+8
48=4x
48/4=x
x=12
The width, which is x, is 12 m. And the length, x+4, is 16 m.
You can check this is correct by calculating the perimeter using those values: 12+12+16+16=56.
You use a modification of the pythagorean theorem to find
pythagoreas c^2=a^2+b^2
the easy way is you use the equation
![d= \sqrt{(x1-x2)^2+(y1-y2)^2}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%7D%20)
so input in format (x,y) then
(2,2)
(7,5)
x1=2
y1=2
x2=7
y2=5
![d= \sqrt{(2-7)^2+(2-5)^2}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%282-7%29%5E2%2B%282-5%29%5E2%7D%20)
![d= \sqrt{(-4)^2+(-3)^2}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%28-4%29%5E2%2B%28-3%29%5E2%7D%20)
![d= \sqrt{16+9}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B16%2B9%7D%20)
![d= \sqrt{25}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B25%7D%20)
![d= 5](https://tex.z-dn.net/?f=d%3D%205%20)
the distance is 5 units
Answer: ![37000+2500n](https://tex.z-dn.net/?f=37000%2B2500n)
Step-by-step explanation:
Given
John makes $82,000 per year after 18 years
If he would have to get a raise of $2500 per year
Suppose he starts with a salary of ![x](https://tex.z-dn.net/?f=x)
after the first year, his salary would be
![\Rightarrow x+2500](https://tex.z-dn.net/?f=%5CRightarrow%20x%2B2500)
After 2 years, the salary would be
![\Rightarrow x+2500+2500=x+2\times 2500](https://tex.z-dn.net/?f=%5CRightarrow%20x%2B2500%2B2500%3Dx%2B2%5Ctimes%202500)
Similarly, after n years salary is
![\Rightarrow x+2500n](https://tex.z-dn.net/?f=%5CRightarrow%20x%2B2500n)
For 18 years, it is
![\Rightarrow x+2500\times 18=82,000\\\Rightarrow c=82,000-45,000=\$\ 37,000](https://tex.z-dn.net/?f=%5CRightarrow%20x%2B2500%5Ctimes%2018%3D82%2C000%5C%5C%5CRightarrow%20c%3D82%2C000-45%2C000%3D%5C%24%5C%2037%2C000)
So, after n years of working salary is ![37,000+2500n](https://tex.z-dn.net/?f=37%2C000%2B2500n)
You can rule out A and C 6/6 makes 1 so that cancels so your answer is D