a triangle has side lengths measuring $3x$ cm, $7x$ cm, and $h$ cm. which expression describes the possible…

a triangle has side lengths measuring $3x$ cm, $7x$ cm, and $h$ cm. which expression describes the possible values of $h$, in cm?\n$4x < h < 10x$\n$10x < h < 4x$\n$h = 4x$\n$h = 10x$

a triangle has side lengths measuring $3x$ cm, $7x$ cm, and $h$ cm. which expression describes the possible values of $h$, in cm?\n$4x < h < 10x$\n$10x < h < 4x$\n$h = 4x$\n$h = 10x$

Answer

Explanation:

Step1: Apply triangle inequality rule

The sum of any two sides of a triangle must be greater than the third side. First, find the lower bound of $h$: subtract the smaller known side from the larger known side. $7x - 3x = 4x$ So $h > 4x$.

Step2: Find upper bound of $h$

Add the two known sides to get the upper limit for $h$. $7x + 3x = 10x$ So $h < 10x$.

Step3: Combine the inequalities

Combine the lower and upper bounds to get the range for $h$.

Answer:

$4x < h < 10x$ (Option A)