Question

What is the perimeter of the isosceles triangle ABC such that angle A= angle C ?

Answer 1

Given angle A=angle C.

The objective is to find the perimeter of the isosceles triangle ABC.

First let's find the value of x.

An isosceles triangle contains two equal sides. Here angle A and angle C are equal. So the sides AB and AC are equal.

`\begin{gathered} AB=BC \\ 5x-1=3x+11 \\ 5x-3x=11+1 \\ 2x=12 \\ x=(12)/(2) \\ x=6 \end{gathered}`

Now, find the perimeter of the triangle by adding all the sides of the triangle.

`P=5x-1+3x+11+x+19`

Substittue the value of x =6.

`\begin{gathered} P=5(6)-1+3(6)+11+6+19 \\ P=30-1+18+11+6+19 \\ P=83 \end{gathered}`

Hence, the perimeter of the triangle is 83.

`\begin{gathered} \text{Let's check the whether the obtained x value if correct.} \\ AB=BC \\ 5x-1=3x+11 \\ 5(6)-1=3(6)+11 \\ 30-1=18+11 \\ 29=29 \end{gathered}`

Thus the sides of isoscles triangles are equal. Hence the value of x is correct.