Write an expression in terms of 𝑥 for the perimeter in centimetres of the isosceles triangle shown below.
We don’t know the value of 𝑥 and we don’t have any information about the perimeter to allow us to find the value of 𝑥, which is why we’ve been asked to find an expression. From the diagram, we can see that we’ve been given information about two of the sides: 𝐵𝐶 is 10 centimetres and 𝐴𝐶 is 𝑥 centimetres.
In order to find an expression for the perimeter, we need to know the length of all three sides, which means we need an expression for side 𝐴𝐵. The key information is in the question. We are told that the triangle is isosceles. The blue lines on two sides of the triangle indicate that these two sides of the triangle are equal to each other. Therefore, the length of side 𝐴𝐵 is the same as the length of side 𝐴𝐶. So 𝐴𝐵 is also 𝑥 centimetres.
Now, we can find our expression for the perimeter of the triangle. To find a perimeter, we need to add together all three sides. The perimeter is 𝐴𝐵 plus 𝐴𝐶 plus 𝐵𝐶, and the units are centimetres. Substituting the length of each side gives that the perimeter is 𝑥 plus 𝑥 plus 10 centimetres. This expression can be simplified by adding the two 𝑥s together to give the final expression for the perimeter of the triangle two 𝑥 plus 10 centimetres.