X = 11
I know for sure. Just did this unit
What is the figure?.......
Answer:
The perimeter of ΔABC is 43 units
Step-by-step explanation:
An illustrative diagram is shown in the attachment below.
To find the perimeter of the triangle, we will first determine the length of the unknown sides.
First, we can determine /BC/ using the Sine rule
From Sine rule
![\frac{SinA}{a} = \frac{SinB}{b} = \frac{SinC}{c}](https://tex.z-dn.net/?f=%5Cfrac%7BSinA%7D%7Ba%7D%20%3D%20%5Cfrac%7BSinB%7D%7Bb%7D%20%3D%20%5Cfrac%7BSinC%7D%7Bc%7D)
∴ ![\frac{SinA}{a} = \frac{SinC}{c}](https://tex.z-dn.net/?f=%5Cfrac%7BSinA%7D%7Ba%7D%20%3D%20%5Cfrac%7BSinC%7D%7Bc%7D)
In the diagram,
and ![c = /AB/ = 12](https://tex.z-dn.net/?f=c%20%3D%20%2FAB%2F%20%3D%2012)
m∠A=60° and m∠C=45°
∴ ![\frac{Sin60}{/BC/} = \frac{Sin45}{12}](https://tex.z-dn.net/?f=%5Cfrac%7BSin60%7D%7B%2FBC%2F%7D%20%3D%20%5Cfrac%7BSin45%7D%7B12%7D)
![/BC/ = \frac{12 \times Sin60}{Sin45}](https://tex.z-dn.net/?f=%2FBC%2F%20%3D%20%5Cfrac%7B12%20%5Ctimes%20Sin60%7D%7BSin45%7D)
![/BC/ = 6\sqrt{6}](https://tex.z-dn.net/?f=%2FBC%2F%20%3D%206%5Csqrt%7B6%7D)
To find /AC/, will first determine m∠B
m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)
60° +m∠B + 45° = 180°
m∠B + 105° = 180°
m∠B = 180° - 105°
m∠B = 75°
Also, using the sine rule
![\frac{SinB}{b} = \frac{SinC}{c}](https://tex.z-dn.net/?f=%5Cfrac%7BSinB%7D%7Bb%7D%20%3D%20%5Cfrac%7BSinC%7D%7Bc%7D)
From the diagram, ![b = /AC/](https://tex.z-dn.net/?f=b%20%3D%20%2FAC%2F)
![\frac{Sin75}{/AC/} = \frac{Sin45}{12}](https://tex.z-dn.net/?f=%5Cfrac%7BSin75%7D%7B%2FAC%2F%7D%20%3D%20%5Cfrac%7BSin45%7D%7B12%7D)
![/AC/ = \frac{12 \times Sin75}{Sin45}](https://tex.z-dn.net/?f=%2FAC%2F%20%3D%20%5Cfrac%7B12%20%5Ctimes%20Sin75%7D%7BSin45%7D)
![/AC/ = 6 + 6\sqrt{3}](https://tex.z-dn.net/?f=%2FAC%2F%20%3D%206%20%2B%206%5Csqrt%7B3%7D)
Now,
The perimeter of ΔABC = /AB/ + /BC/ + /AC/
= ![12 + 6\sqrt{6} + 6+6\sqrt{3}](https://tex.z-dn.net/?f=12%20%2B%206%5Csqrt%7B6%7D%20%2B%206%2B6%5Csqrt%7B3%7D)
= 43.09 units
≅ 43 units
Hence, the perimeter of ΔABC is 43 units.
The answer to this is 2. Ten only has two factors, 5 and 2, and 2 can be decided evenly amongst them all.