A=B H
area equals the base times the height
Answer:
a) Area of a rectangle = length × width
Area = 6138cm²
Width = 62m
length = Area / width
length = 6138/62
length = 99m
b) Perimeter of a rectangle = 2l + 2w
l = length
w = width
perimeter = 338m
length = 98m
338 = 2(98) + 2w
2w = 338 - 196
2w = 142
w = 71m
width = 71m
Hope this helps.
let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.
![\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bhyperbolas%2C%20vertical%20traverse%20axis%20%7D%20%5C%5C%5C%5C%20%5Ccfrac%7B%28y-%20k%29%5E2%7D%7B%20a%5E2%7D-%5Ccfrac%7B%28x-%20h%29%5E2%7D%7B%20b%5E2%7D%3D1%20%5Cqquad%20%5Cbegin%7Bcases%7D%20center%5C%20%28%20h%2C%20k%29%5C%5C%20vertices%5C%20%28%20h%2C%20k%5Cpm%20a%29%5C%5C%20c%3D%5Ctextit%7Bdistance%20from%7D%5C%5C%20%5Cqquad%20%5Ctextit%7Bcenter%20to%20foci%7D%5C%5C%20%5Cqquad%20%5Csqrt%7B%20a%20%5E2%20%2B%20b%20%5E2%7D%5C%5C%20asymptotes%5Cquad%20y%3D%20k%5Cpm%20%5Ccfrac%7Ba%7D%7Bb%7D%28x-%20h%29%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}](https://tex.z-dn.net/?f=%5Ccfrac%7B%28y-3%29%5E2%7D%7B1%7D-%5Ccfrac%7B%28x%2B2%29%5E2%7D%7B4%7D%3D1%5Cimplies%20%5Ccfrac%7B%5By-3%5D%5E2%7D%7B1%5E2%7D-%5Ccfrac%7B%5Bx-%28-2%29%5D%5E2%7D%7B2%5E2%7D%3D1~~%20%5Cbegin%7Bcases%7D%20h%3D-2%5C%5C%20k%3D3%5C%5C%20a%3D1%5C%5C%20b%3D2%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5Cimplies%20c%3D%5Csqrt%7B1%2B4%7D%5Cimplies%20c%3D%5Csqrt%7B5%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bso%20then%20the%20foci%20are%20at%7D%7D%7B%28-2~~%2C~~3%5Cpm%20%5Csqrt%7B5%7D%29%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Band%20its%20vertices%20are%20at%20%7D%7D%7B%28-2~~%2C~~3%5Cpm%201%29%7D%5Cimplies%20%5Cbegin%7Bcases%7D%20%28-2%2C4%29%5C%5C%20%28-2%2C2%29%20%5Cend%7Bcases%7D)
now let's check for the asymptotes.
![\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2](https://tex.z-dn.net/?f=%5Cbf%20y%3D3%5Cpm%20%5Ccfrac%7B1%7D%7B2%7D%5Bx-%28-2%29%5D%5Cimplies%20y%3D3%5Cpm%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20y%3D3%2B%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%5Cimplies%20y%3D3%2B%5Ccfrac%7Bx%2B2%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B6%2Bx%2B2%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7Bx%2B8%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B1%7D%7B2%7Dx%2B4%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20y%3D3-%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%5Cimplies%20y%3D3-%5Ccfrac%7B%28x%2B2%29%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B6-%28x%2B2%29%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7B6-x-2%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B-x%2B4%7D%7B2%7D%5Cimplies%20y%3D-%5Ccfrac%7B1%7D%7B2%7Dx%2B2)
Answer:
A=582.94, so 583.
Step-by-step explanation:
<em>MERRY CHRISTMAS,</em>
<em>Hope that helped :)</em>