Question

28. The legs of an isosceles triangle have lengths 3x + 4 and x + 18.The base has length x + 2. What is the length of the base?A. 9B. 25C. 7D. cannot be determined

Answer 1

An isosceles triangle is a triangle that has two legs of equal length.

So, to find the length of the base, follow the steps below.

Step 01: Equal the legs lengths.

Since the legs have the same length:

`3x+4=x+18`

Step 02: Isolate x.

To do it, first, subtract x from both sides.

`\begin{gathered} 3x+4-x=x+18-x \\ 3x-x+4=x-x+18 \\ 2x+4=18 \end{gathered}`

Now, subtract 4 from both sides.

`\begin{gathered} 2x+4-4=18-4 \\ 2x=14 \end{gathered}`

Finally, divide both sides by 2.

`\begin{gathered} (2x)/(2)=(14)/(2) \\ x=7 \end{gathered}`

Step 03: Find the length of the base.

Knowing that x = 7, substitute x in x + 2 and find the lenght.

`\begin{gathered} \text{base}=x+2 \\ base=7+2 \\ base=9 \end{gathered}`

Answer: A. 9.