Question

Consider the triangle below.Part A: If AMG is an isosceles triangle with base AG, what is the value of x? Justify youranswerPart B: What is the length of each leg?Part C: What is the length of the base ?

Answer 1

In a isosceles triangle, the sides that are not the base are called legs and have the same length.

Since AG is the base, than the legd are MG and GA, which by definition will have the same lengths.

Thus, we can set the exporession for each equal to one another:

`\begin{gathered} (x+1.4)in=(2x+0.1)in \\ x+1.4=2x+0.1 \\ 1.4-0.1=2x-x \\ 1.3=x \\ x=1.3 \end{gathered}`

Part A: So, the value of x is 1.3.

Now, we can input x into the expression for either leg to get its value:

`(x+1.4)in=(1.3+1.4)in=2.7in`

We don't need, but we can check if it is correct for the other:

`(2x+0.1)in=(2\cdot1.3+0.1)in=(2.6+0.1)in=2.7in`

Part B: Thus, the length of each leg is 2.7 in.

And to calculate the length of the base, we put x into the expression for the base:

`(3x-0.4)in=(3\cdot1.3-0.4)in=(3.9-0.4)in=3.5in`

Part C: Thus, the length of the base is 3.5 in.