Question

sides of a triangle practice complete this assessment to review what youve learned. it will not count toward your grade. use the image to answer the question. x is the length in inches of the third side of a triangle. the range of all possible values of x is shown on the number line. which of the following options has possible lengths of the other two sides of the triangle? (1 point) 42 inches and 50 inches 28 inches and 64 inches 36 inches and 92 inches 48 inches and 76 inches

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side $x$ of a triangle with side lengths $a$ and $b$ satisfies the inequalities $|a - b|\lt x\lt a + b$.

Step2: Check option A

For $a = 42$ and $b = 50$, $|42-50|=8$ and $42 + 50=92$. The range of the third - side is $8\lt x\lt92$. But the given range for $x$ is $36\lt x\lt92$, so this option is not correct as the lower - bound is not $36$.

Step3: Check option B

For $a = 28$ and $b = 64$, $|28 - 64|=36$ and $28+64 = 92$. The range of the third - side is $36\lt x\lt92$, which matches the given range for $x$ on the number line.

Step4: Check option C

For $a = 36$ and $b = 92$, $|36 - 92|=56$ and $36+92 = 128$. The range of the third - side is $56\lt x\lt128$, which does not match the given range for $x$.

Step5: Check option D

For $a = 48$ and $b = 76$, $|48 - 76|=28$ and $48+76 = 124$. The range of the third - side is $28\lt x\lt124$, which does not match the given range for $x$.

Answer:

B. 28 inches and 64 inches