The perimeter of the equilateral triangle is 3s and s=4x so the perimeter is:
12x
And we are told that the perimeter of the square is the same. And that perimeter is 4s where s=(x+6) so that perimeter is equal to
4x+24, and again, we are told that these two values are equal so we can solve for x...
12x=4x+24
8x=24
x=3 and if x=3 then the side length is (x+6)=9
So the area of the square is always A=s^2 and s=9 thus:
A=9^2
A=81 u^2
![\bf \textit{perimeter of a rectangle}=p=side+side+side+side \\\\ or\implies p=w+w+l+l\implies p=2w+2l \\\\ p=2(w+l)\qquad \begin{cases} w=width\\ l=length\\ ------\\ p=48 \end{cases}\implies 40=2(w+l)\\\\ -----------------------------\\\\ \textit{area of it}=A=w\cdot l\qquad \begin{cases} w=width\\ l=length\\ ------\\ A=40 \end{cases}\implies 40=wl\\\\ -----------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bperimeter%20of%20a%20rectangle%7D%3Dp%3Dside%2Bside%2Bside%2Bside%0A%5C%5C%5C%5C%0Aor%5Cimplies%20p%3Dw%2Bw%2Bl%2Bl%5Cimplies%20p%3D2w%2B2l%0A%5C%5C%5C%5C%0Ap%3D2%28w%2Bl%29%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Aw%3Dwidth%5C%5C%0Al%3Dlength%5C%5C%0A------%5C%5C%0Ap%3D48%0A%5Cend%7Bcases%7D%5Cimplies%2040%3D2%28w%2Bl%29%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ctextit%7Barea%20of%20it%7D%3DA%3Dw%5Ccdot%20l%5Cqquad%20%5Cbegin%7Bcases%7D%0Aw%3Dwidth%5C%5C%0Al%3Dlength%5C%5C%0A------%5C%5C%0AA%3D40%0A%5Cend%7Bcases%7D%5Cimplies%2040%3Dwl%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%20)
![\bf thus\qquad \begin{cases} 40=2(w+l)\to \frac{40}{2}=w+l\to\frac{40}{2}-l=\boxed{w} \\\\ 40=wl\\ --------------\\ 40=\left( \boxed{\frac{40}{2}-l} \right)\cdot l \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20thus%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0A40%3D2%28w%2Bl%29%5Cto%20%5Cfrac%7B40%7D%7B2%7D%3Dw%2Bl%5Cto%5Cfrac%7B40%7D%7B2%7D-l%3D%5Cboxed%7Bw%7D%0A%5C%5C%5C%5C%0A40%3Dwl%5C%5C%0A--------------%5C%5C%0A40%3D%5Cleft%28%20%5Cboxed%7B%5Cfrac%7B40%7D%7B2%7D-l%7D%20%5Cright%29%5Ccdot%20l%0A%5Cend%7Bcases%7D)
solve for "l" to find its length
Answer:
5 years
Step-by-step explanation:
The shorter tree is 5 ft shorter, but is growing 1 ft/year faster. It will make up the difference of 5 ft in (5 ft)/(1 ft/year) = 5 years.
I believe there has to be an image included with this question my friend. Thine error hath been made known by the supreme lord of dao.
Answer is A. It is the center of the circle that can be inscribed in a given triangle
Explanation
The circumcenter is called ”the circumcenter” because it is the center of the circle that ”circumscribes” the triangle.