Answer:
![\frac{ \sqrt{6} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20)
Step-by-step explanation:
To find side x , since it the shortest side. Divide the second longest side by sqr root of 3.
Why?
This is a 30-60-90 triangle so that means the second longest side will be sqr root of 3 times more than the shortest side
![\sqrt{2} \div \sqrt{3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B2%7D%20%20%5Cdiv%20%20%5Csqrt%7B3%7D%20)
![\frac{ \sqrt{2} }{1} \times \frac{1}{ \sqrt{3} } = \frac{ \sqrt{2} }{ \sqrt{3} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B1%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20)
RATIONALIZE the denominator
![\frac{ \sqrt{2} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ \sqrt{6} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%20%20%5Ctimes%20%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20)
Sqr root of 6 over 3 is the answer.
This section is extra If you want to.
Since the longest side is twice the shortest side, the longest side is
![\frac{2 \sqrt{6} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20)
Let proof
using pythagorean theorem,
![( \frac{ \sqrt{6} }{3} ) {}^{2} + (\sqrt{2} ) {}^{2}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20%29%20%7B%7D%5E%7B2%7D%20%20%2B%20%20%28%5Csqrt%7B2%7D%20%29%20%7B%7D%5E%7B2%7D%20)
![\frac{6}{9} + 2 = \frac{24}{9}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B9%7D%20%20%2B%202%20%3D%20%20%5Cfrac%7B24%7D%7B9%7D%20)
![\sqrt{ \frac{ {24} }{9} } = \frac{2 \sqrt{6} }{3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7B%20%7B24%7D%20%7D%7B9%7D%20%7D%20%20%3D%20%20%5Cfrac%7B2%20%5Csqrt%7B6%7D%20%7D%7B3%7D%20)
So it is right.
Answer: This quadrilateral is not a parallelogram because 1. opposite sides are not equal and 2. the right and left sides are not parallel.
Step-by-step explanation:
1. The top side is 4 units long and the bottom side is 8 units long. 4
8.
2. The side on the left has a slope of 5/13 while the side on the right has a slope of 5/9.
Answer:
4 ft
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
9 = 1/2 (4.5)h
9 =2.25 h
Divide each side by 2.25
9/2.25 = 2.25h/2.25
4 =h
Answer:
AAS
Step-by-step explanation: