The answer is 6.85.
Consider, x-y axis, and side of equilateral triangle is ' a '.
Given,
![$$\begin{aligned}&A P=3 \text { units } \\&B P=2 \text { units } \\&C P=4 \text { units }\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%26A%20P%3D3%20%5Ctext%20%7B%20units%20%7D%20%5C%5C%26B%20P%3D2%20%5Ctext%20%7B%20units%20%7D%20%5C%5C%26C%20P%3D4%20%5Ctext%20%7B%20units%20%7D%5Cend%7Baligned%7D%24%24)
Let x and y are point in x-y axis.
Using, distance formula here
![$A P^{2}=(x-0)^{2}+(y-0)^{2}$](https://tex.z-dn.net/?f=%24A%20P%5E%7B2%7D%3D%28x-0%29%5E%7B2%7D%2B%28y-0%29%5E%7B2%7D%24)
![$3^{2}=x^{2}+y^{2}$](https://tex.z-dn.net/?f=%243%5E%7B2%7D%3Dx%5E%7B2%7D%2By%5E%7B2%7D%24)
__________(i)
![$p c^{2}=(x-a)^{2}+(y-0)^{2}$$4^{2}=x^{2}-2 a x+a^{2}+y^{2}$](https://tex.z-dn.net/?f=%24p%20c%5E%7B2%7D%3D%28x-a%29%5E%7B2%7D%2B%28y-0%29%5E%7B2%7D%24%244%5E%7B2%7D%3Dx%5E%7B2%7D-2%20a%20x%2Ba%5E%7B2%7D%2By%5E%7B2%7D%24)
from (i)
![$16=x^{2} 9-2 a x+a^{2}$](https://tex.z-dn.net/?f=%2416%3Dx%5E%7B2%7D%209-2%20a%20x%2Ba%5E%7B2%7D%24)
![$2 a x=a^{2}+9-16$](https://tex.z-dn.net/?f=%242%20a%20x%3Da%5E%7B2%7D%2B9-16%24)
![$\left[x=\frac{\left(a^{2}-7\right)}{2 a}\right]$](https://tex.z-dn.net/?f=%24%5Cleft%5Bx%3D%5Cfrac%7B%5Cleft%28a%5E%7B2%7D-7%5Cright%29%7D%7B2%20a%7D%5Cright%5D%24)
![$B p^{2}=\left(x-\frac{a}{2}\right)^{2}+\left(y-\frac{\sqrt{3}}{2} a\right)^{2}$](https://tex.z-dn.net/?f=%24B%20p%5E%7B2%7D%3D%5Cleft%28x-%5Cfrac%7Ba%7D%7B2%7D%5Cright%29%5E%7B2%7D%2B%5Cleft%28y-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20a%5Cright%29%5E%7B2%7D%24)
![$2^{2}=x^{2}-a x+\frac{a^{2}}{4}+y^{2}-\sqrt{3} a b y+\frac{3}{4} a^{2}$](https://tex.z-dn.net/?f=%242%5E%7B2%7D%3Dx%5E%7B2%7D-a%20x%2B%5Cfrac%7Ba%5E%7B2%7D%7D%7B4%7D%2By%5E%7B2%7D-%5Csqrt%7B3%7D%20a%20b%20y%2B%5Cfrac%7B3%7D%7B4%7D%20a%5E%7B2%7D%24)
![$4=\left(x^{2}+y^{2}\right)+\frac{a^{2}+3 a^{2}}{4}-a\left(\frac{a^{2}-7}{2 a}\right)-\sqrt{3} a y$](https://tex.z-dn.net/?f=%244%3D%5Cleft%28x%5E%7B2%7D%2By%5E%7B2%7D%5Cright%29%2B%5Cfrac%7Ba%5E%7B2%7D%2B3%20a%5E%7B2%7D%7D%7B4%7D-a%5Cleft%28%5Cfrac%7Ba%5E%7B2%7D-7%7D%7B2%20a%7D%5Cright%29-%5Csqrt%7B3%7D%20a%20y%24)
from (i)
![$4=9+a^{2}-a^{2}+7-\sqrt{3} a y$](https://tex.z-dn.net/?f=%244%3D9%2Ba%5E%7B2%7D-a%5E%7B2%7D%2B7-%5Csqrt%7B3%7D%20a%20y%24)
![$\sqrt{3} a y=16-4$](https://tex.z-dn.net/?f=%24%5Csqrt%7B3%7D%20a%20y%3D16-4%24)
put x and y in equarion_______(i)
![$\left(\frac{12}{\sqrt{3} a}\right)^{2}+\left(\frac{a^{2}-7}{2 a}\right)^{2}=9$](https://tex.z-dn.net/?f=%24%5Cleft%28%5Cfrac%7B12%7D%7B%5Csqrt%7B3%7D%20a%7D%5Cright%29%5E%7B2%7D%2B%5Cleft%28%5Cfrac%7Ba%5E%7B2%7D-7%7D%7B2%20a%7D%5Cright%29%5E%7B2%7D%3D9%24)
![$\frac{144}{3 a^{2}}+\frac{\left(a^{2}-7\right)^{2}}{4 a^{2}}=9$](https://tex.z-dn.net/?f=%24%5Cfrac%7B144%7D%7B3%20a%5E%7B2%7D%7D%2B%5Cfrac%7B%5Cleft%28a%5E%7B2%7D-7%5Cright%29%5E%7B2%7D%7D%7B4%20a%5E%7B2%7D%7D%3D9%24)
![$144 \times 4+3\left(a^{2}-7\right)^{2}=12 \times 9 a^{2}$](https://tex.z-dn.net/?f=%24144%20%5Ctimes%204%2B3%5Cleft%28a%5E%7B2%7D-7%5Cright%29%5E%7B2%7D%3D12%20%5Ctimes%209%20a%5E%7B2%7D%24)
![$576+3\left(a^{2}-7\right)^{2}=108 a^{2}$](https://tex.z-dn.net/?f=%24576%2B3%5Cleft%28a%5E%7B2%7D-7%5Cright%29%5E%7B2%7D%3D108%20a%5E%7B2%7D%24)
![put $a^{2}=t$$$576+3(t-7)^{2}=108 t$$](https://tex.z-dn.net/?f=put%20%24a%5E%7B2%7D%3Dt%24%24%24576%2B3%28t-7%29%5E%7B2%7D%3D108%20t%24%24)
![$\begin{aligned} 576+3\left(t^{2}-14 t+49\right) &=108 t \\ 576+3 t^{2}-42 t+147 &=108 t \end{aligned}$](https://tex.z-dn.net/?f=%24%5Cbegin%7Baligned%7D%20576%2B3%5Cleft%28t%5E%7B2%7D-14%20t%2B49%5Cright%29%20%26%3D108%20t%20%5C%5C%20576%2B3%20t%5E%7B2%7D-42%20t%2B147%20%26%3D108%20t%20%5Cend%7Baligned%7D%24)
![$3 t^{2}-150 t+429=0$$t^{2}-50 t+143=0$$t=50 \pm \sqrt{50^{2}-4 \times 143}$](https://tex.z-dn.net/?f=%243%20t%5E%7B2%7D-150%20t%2B429%3D0%24%24t%5E%7B2%7D-50%20t%2B143%3D0%24%24t%3D50%20%5Cpm%20%5Csqrt%7B50%5E%7B2%7D-4%20%5Ctimes%20143%7D%24)
![t=\frac{50 \pm \sqrt{1928}}{2}t=\frac{50 \pm 43.91}{2}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B50%20%5Cpm%20%5Csqrt%7B1928%7D%7D%7B2%7Dt%3D%5Cfrac%7B50%20%5Cpm%2043.91%7D%7B2%7D)
![t=\frac{50 \pm 43.91}{2}\\t=46.9545, \quad t=3.0455](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B50%20%5Cpm%2043.91%7D%7B2%7D%5C%5Ct%3D46.9545%2C%20%5Cquad%20t%3D3.0455)
![$\begin{array}{ll}a^{2}=46.9545, \\ a=\sqrt{46.9545}, & a^{2}=3.0455 \\ a, a=1.745\end{array}$](https://tex.z-dn.net/?f=%24%5Cbegin%7Barray%7D%7Bll%7Da%5E%7B2%7D%3D46.9545%2C%20%5C%5C%20a%3D%5Csqrt%7B46.9545%7D%2C%20%26%20a%5E%7B2%7D%3D3.0455%20%5C%5C%20a%2C%20a%3D1.745%5Cend%7Barray%7D%24)
![$a=6.85$](https://tex.z-dn.net/?f=%24a%3D6.85%24)
for this point P is outside Therefore, it is not consider as solution (because in question inside point ls mention)
![a=6.85 units](https://tex.z-dn.net/?f=a%3D6.85%20units)
What is equilateral triangle?
- A triangle with the same length on all three sides
- If all of the sides of a form are the same length, it is said to be equilateral. Many forms, such as triangles and squares, are covered in geometry instruction.
- Because all of the sides of a square have the same length, it is equilateral.
To learn more about equilateral triangle visit:
brainly.com/question/3461022
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You multiply 20,400 by 10 which will equal 204,000
Answer:
r = 3 scoop de whoop
Step-by-step explanation:
36 ÷ 12 = 3
Answer:
5.25x - 6
Step-by-step explanation:
<u>1.75x</u> -2 + <u>1.75x</u> -2 + <u>1.75x </u>-2
5.25x <u>- 2 - 2 - 2</u>
5.25x - 6
Answer:
d
Step-by-step explanation:
f(3)=5(3)²-7(4(3)+3))
=45-105
= -60