Question

An isosceles triangle has two sides of equal length. The third side is five less than twice the length of one of the other sides. If the perimeter of the triangle is 23 cm what is the length of the third side?

Answer 1

9 cm

Explanation:

Let's say that the length of the 2 equal sides is x.

That means:

Side 1 = x

Side 2 = x

We know that the third side is 5 less than twice the length of the 2 equal sides, or 2x-5

Side 3 = 2x-5

The perimeter is all sides together.

Side 1 + Side 2 + Side 3

We know the length of each side, so let's put that in instead.

x + x + 2x-5

Let's simplify this expression:

x + x + 2x - 5

2x + 2x - 5

4x - 5

We know the perimeter, 4x-5, is 23 cm.

4x - 5 = 23

4x = 28

x = 7

The third side is 2x-5. If x is 7...

2*7 - 5 = 14-5 = 9

Answer: 9 cm

Answer 2

9

Explanation:

We can set up a systems of equations to find the value of the third side.

Let's assume that
`x` is the length of both sides 1 and 2. Let's also assume that
`y` is the length of the third side.

We know that
`x + x + y = 23`, and looking at the first clue we can make the equation
`y = 2x-5`.

We can substitute y into the equation
`x + x + y = 23`.

`x + x + (2x-5) = 23\\\\2x + 2x-5 = 23\\4x-5 = 23\\4x = 28\\x = 7`

So the length of the side that is the same as the second is 7.

Now we can plug this into the equation
`y = 2x-5` to find
`y`.

`y = 2(7) - 5\\\\y = 14-5\\\\y = 9`

Hope this helped!