The perimeter will also be scaled down by half if the original triangle if it were scaled down by half.
<h3>What is the perimeter of a triangle?</h3>
The total length of a triangle's boundary is referred to as its perimeter. It is the total of the triangle's three sides. A triangle's perimeter will be equal to a+b+c if its three sides are a, b, and c.
The sides of the original triangle are:
x+3, 2x+4, 3x-1
The perimeter of the triangle will be
![x+3+2x+4+3x-1\\=6x+6](https://tex.z-dn.net/?f=x%2B3%2B2x%2B4%2B3x-1%5C%5C%3D6x%2B6)
If it were scaled down by half then new sides will be
![\frac{x+3}{2} , \frac{2x+4}{2} , \frac{x-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B3%7D%7B2%7D%20%2C%20%5Cfrac%7B2x%2B4%7D%7B2%7D%20%2C%20%5Cfrac%7Bx-1%7D%7B2%7D)
So, the perimeter of the new triangle will be
![\frac{x+3}{2} + \frac{2x+4}{2} + \frac{3x-1}{2}\\=\frac{x+3+2x+4+3x-1}{2} \\=\frac{6x+6}{2}\\ =3x+3](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B3%7D%7B2%7D%20%2B%20%5Cfrac%7B2x%2B4%7D%7B2%7D%20%2B%20%5Cfrac%7B3x-1%7D%7B2%7D%5C%5C%3D%5Cfrac%7Bx%2B3%2B2x%2B4%2B3x-1%7D%7B2%7D%20%5C%5C%3D%5Cfrac%7B6x%2B6%7D%7B2%7D%5C%5C%20%3D3x%2B3)
This is half of the original triangle's perimeter. Therefore, the perimeter of the new triangle is half of the perimeter of the original triangle.
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Let width = x then
2x+ 2(x + 2) = 80
4x + 4 = 80
4x = 76
x = 19
so the width is 19 and the length is 21 answer
Find the cube root of 90 if there isn't, try to compare irrational numbers
Answer:
The equation of the perpendicular bisector line
5 x - 2 y + 31 =0
Step-by-step explanation:
<u><em> Explanation:-</em></u>
Given points are ( 0,1) and (-10,5)
The Midpoint of given two points
![(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx_%7B1%7D%2Bx_%7B2%7D%20%20%7D%7B2%7D%20%2C%20%5Cfrac%7By_%7B1%7D%2By_%7B2%7D%20%20%7D%7B2%7D%20%29)
(-5 , 3)
The Slope of the line
m = ![\frac{y_{2} -y_{1} }{x_{2}-x_{1} } = \frac{5-1}{-10} = \frac{-2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D%20-y_%7B1%7D%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D%20%3D%20%5Cfrac%7B5-1%7D%7B-10%7D%20%3D%20%5Cfrac%7B-2%7D%7B5%7D)
The perpendicular slope
= ![\frac{-1}{m} = \frac{-1}{\frac{-2}{5} } = \frac{5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7Bm%7D%20%3D%20%5Cfrac%7B-1%7D%7B%5Cfrac%7B-2%7D%7B5%7D%20%7D%20%3D%20%5Cfrac%7B5%7D%7B2%7D)
The equation of the perpendicular bisector line
![y - y_{1} = m (x - x_{1} )](https://tex.z-dn.net/?f=y%20-%20y_%7B1%7D%20%3D%20m%20%28x%20-%20x_%7B1%7D%20%29)
![y - 3 = \frac{5}{2} ( x-(-5))](https://tex.z-dn.net/?f=y%20-%203%20%3D%20%5Cfrac%7B5%7D%7B2%7D%20%28%20x-%28-5%29%29)
2 y - 6 = 5( x +5)
5 x + 25 -2y +6 =0
5 x - 2 y + 31 =0