<h2>=>> <u>Solution (part A</u>) :</h2>
Given :
▪︎Triangle AMG is an isosceles triangle.
▪︎Measure of segment AM = (x+1.4) inches
▪︎Measure of segment MG = (2x+0.1) inches
▪︎Measure of segment AG = (3x-0.4) inches
▪︎segment AG is the base of triangle AMG.
Since AG is the base of the isosceles triangle AMG, segment AM and segment MG will be equal.
Which means :
![= \tt x + 1.4 = 2x + 0.1](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20x%20%2B%201.4%20%3D%202x%20%2B%200.1)
![= \tt x + 1.4 - 0.1 = 2x](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20x%20%2B%201.4%20-%200.1%20%3D%202x)
![= \tt \: x + 1.3 = 2x](https://tex.z-dn.net/?f=%20%3D%20%20%5Ctt%20%5C%3A%20x%20%2B%201.3%20%3D%202x)
![= \tt 1.3 = 2x - x](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%201.3%20%3D%202x%20-%20x)
![\color{plum} \hookrightarrow \tt x = 1.3](https://tex.z-dn.net/?f=%20%5Ccolor%7Bplum%7D%20%5Chookrightarrow%20%20%5Ctt%20x%20%3D%201.3)
Thus, the value of x = 1.3
Therefore :
▪︎The value of x = 1.3
<h2>=>> <u>
Solution (Part B)</u> :</h2>
We know that :
▪︎The value of x = 1.3
Which means :
The length of the leg AM :
![= \tt x + 1.4](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20x%20%2B%201.4)
![= \tt 1.3 + 1.4](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%201.3%20%2B%201.4)
![\color{plum} \tt leg \: AM= 2.7 \: inches](https://tex.z-dn.net/?f=%20%5Ccolor%7Bplum%7D%20%5Ctt%20leg%20%5C%3A%20AM%3D%202.7%20%5C%3A%20inches)
Thus, the length of the leg AM = 2.7 inches
The length of leg MG :
![= \tt 2x + 0.1](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%202x%20%2B%200.1)
![= \tt2 \times 1.3 + 0.1](https://tex.z-dn.net/?f=%20%3D%20%20%5Ctt2%20%5Ctimes%201.3%20%2B%200.1)
![= \tt 2.6 + 0.1](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%202.6%20%2B%200.1)
![\color{plum} \tt\: leg \:MG = 2.7 \: inches](https://tex.z-dn.net/?f=%20%5Ccolor%7Bplum%7D%20%5Ctt%5C%3A%20leg%20%5C%3AMG%20%3D%202.7%20%5C%3A%20inches)
Thus, the length of the leg MG = 2.7 inches
Since the measure of the two legs are equal (2.7=2.7), we can conclude that we have found out the correct length of each leg.
Therefore :
▪︎Measure of leg AM = 2.7 inches
▪︎Measure of leg MG = 2.7 inches
<h2>=>
> <u>Solution </u><u>(</u><u>part C</u><u>)</u> :</h2>
We know that :
Value of x = 1.3
Then, measure of the base AG :
![= \tt 3x - 0.4](https://tex.z-dn.net/?f=%20%3D%20%20%5Ctt%203x%20-%200.4)
![= \tt 3 \times 1.3 - 0.4](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%203%20%5Ctimes%201.3%20-%200.4)
![= \tt 3.9 - 0.4](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%203.9%20-%200.4)
![\color{plum}\tt \: Base \: AG = 3.5 \: inches](https://tex.z-dn.net/?f=%20%20%5Ccolor%7Bplum%7D%5Ctt%20%5C%3A%20Base%20%20%5C%3A%20AG%20%3D%203.5%20%5C%3A%20%20inches)
Thus, the measure of the base = 3.5 inches
Therefore :
▪︎ the length of base AG = 3.5 inches.