Question

in each figure below, the segments on the sides can be moved. create the following triangles, if possible. first figure: a triangle with side lengths of 5, 7, and 8. second figure: a triangle with side lengths of 2, 4, and 7. if there is no triangle possible with the given side lengths, click on
o triangle possible\.

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check the first set of side - lengths (5, 7, 8)

$5 + 7=12>8$, $5 + 8 = 13>7$, $7+8 = 15>5$. So, a triangle with side - lengths 5, 7, and 8 is possible.

Step3: Check the second set of side - lengths (2, 4, 7)

$2+4 = 6<7$. So, a triangle with side - lengths 2, 4, and 7 is not possible.

Answer:

First figure: Triangle is possible.
Second figure: No triangle possible.