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3 years ago

The Three sides of a triangle are, n, 4n-2, 4n-7. if the perimeter of the traingle is 45cm, what is the length of each side?

Mathematics

2 answers:

kogti [31]3 years ago

4 0

Answer:

Step-by-step explanation:

stealth61 [152]3 years ago

3 0

Well to start, we need to combine like terms all the equations together , so
n+ 4n+4n = 9n
-2-7 = -9
put them together and it’s
9n - 9
the perimeter is 45 so
9n - 9 = 45
+9 +9
——————
9n = 54
——————-
9 9
Then the 9 cancels, drop down the n and divide 54/9 and you get

n = 6

and that’s the answer
to prove it
you can do
4(6) - 2 = 22
4(6) - 7 = 17
+ 6 because you just replace the n with 6
Add them...
22+17+6 = 45
and so now we know for sure the value of n is 6!

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$\begin{gathered} A=\text{ 12}\degree \\ B=\text{ 114}\degree \\ C=54\degree \end{gathered}$

Step-by-step explanation:

To calculate the angles of the given triangle, we can use the law of cosines:

$\begin{gathered} \cos (C)=\frac{a^2+b^2-c^2}{2ab} \\ \cos (A)=\frac{b^2+c^2-a^2}{2bc} \\ \cos (B)=\frac{c^2+a^2-b^2}{2ca} \end{gathered}$

Then, given the sides a=2, b=9, and c=8.

$\begin{gathered} \cos (A)=\frac{9^2+8^2-2^2}{2\cdot9\cdot8} \\ \cos (A)=\frac{141}{144} \\ A=\cos ^{-1}(\frac{141}{144}) \\ A=11.7 \\ \text{ Rounding to the nearest degree:} \\ A=12º \end{gathered}$

For B:

$\begin{gathered} \cos (B)=\frac{8^2+2^2-9^2}{2\cdot8\cdot2} \\ \cos (B)=\frac{13}{32} \\ B=\cos ^{-1}(\frac{13}{32}) \\ B=113.9\degree \\ \text{Rounding:} \\ B=114\degree \end{gathered}$ $\begin{gathered} \cos (C)=\frac{2^2+9^2-8^2}{2\cdot2\cdot9} \\ \cos (C)=\frac{21}{36} \\ C=\cos ^{-1}(\frac{21}{36}) \\ C=54.3 \\ \text{Rounding:} \\ C=\text{ 54}\degree \end{gathered}$

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1 year ago

The Three sides of a triangle are, n, 4n-2, 4n-7. if the perimeter of the traingle is 45cm, what is the length of each side?​

The Three sides of a triangle are, n, 4n-2, 4n-7. if the perimeter of the traingle is 45cm, what is the length of each side?