Question

In a certain triangle x,y,z represents side lengths if x=7 and z=5 what must be true about y

Answer 1

`2 < y < 12`

Explanation:

Given

`x = 7`

`z = 5`

Required

What must be true about y?

To answer this, we first calculate the range as follows;

`Minimum = |x - z|`

and

`Maximum = |x + z|`

For Minimum, we have:

`Minimum = |7 - 5|`

`Minimum = |2|`

`Minimum = 2`

For Maximum, we have:

`Maximum = |7 + 5|`

`Maximum = |12|`

`Maximum = 12`

The values of y are then bounded by the following:

`Minimum < y < Maximum`

This gives

`2 < y < 12`