Isosceles triangle equal sides 2x and x + 7

Step by step

The question

Question: find x and the length of the marked sides.

An isosceles triangle has sides 2x and x + 7.

1 Use the isosceles fact

Isosceles means two sides are equal.

The marks show which two.

So the two marked sides are equal: 2x = x + 7.

Careful!

The marks say the sides are the same length.

So we write one equals the other.

2 Get x on one side

There is x on both sides.

We want x on one side only.

So we remove the x from the right side.

To remove x, we take away x.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

x and − x make zero.

Cross them out.

2x − x = x.

So x = 7!

3 Find the side

Put x = 7 in the side 2x.

So each marked side is 14.

4 Check

Let's check: put x = 7 in the other side, x + 7.

We get 14 again: the sides are equal.

So x = 7 is right!

Let's look back.

First: use the isosceles fact.

Then: get x on one side.

Then: find the side.

Last: check.