Question

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm? 4x < h < 10x 10x < h < 4x h = 4x h = 10x

Answer 1

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Three conditions mus be satisfied

Condition N
`1`

`3x+7x > h\\ 10x > h\\h< 10x`

Condition N
`2`

`3x+h > 7x\\ h > 7x-3x\\h> 4x`

Condition N
`3`

`7x+h > 3x\\ h > 3x-7x\\h> -4x` (condition N 3 is included in condition N 2)

therefore

`h> 4x\\ h< 10x\\ 4x < h < 10x`

the answer is the option

4x < h < 10x