Question

The perimeters of the triangles shown below are equal

Using this information, what is the value of x?

Answer 1

`x=19`

Explanation:

The perimeter of a shape is the sum of all of its side lengths. Therefore, the perimeter of the first triangle is
`x-7+x-7+x-7=3x-21` and the perimeter of the second triangle is
`9+15+12=36`.

We are given that the perimeters of the triangles are equal, so
`3x-21` equals
`36`. As an equation, that would be
`3x-21=36`. Solving for
`x`, we get:

`3x-21=36`

`3x=57` (Add
`21` to both sides of the equation to isolate
`x`)

`x=19` (Divide both sides of the equation by
`3` to get rid of
`x`'s coefficient)

Hope this helps!

Answer 2

x=19

Explanation:

The perimeter of the right triangle is

P=9+12+15 =36

The perimeter of the left triangle is

P =x-7+ x-7+ x-7 = 3x-21

Set them equal

36 = 3x-21

Add 21 to each side

36+21 = 3x-21+21

57 = 3x

Divide each side by 3

57/3 = 3x/3

19 =x