Question

select all the sets of side lengths that could form a triangle.
8 feet, 7 feet, 10 feet
9 feet, 4 feet, 5 feet
10 feet, 7 feet, 4 feet
12 feet, 5 feet, 6 feet
13 feet, 8 feet, 4 feet

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 8 feet, 7 feet, 10 feet

$8 + 7=15>10$, $8 + 10 = 18>7$, $7+10 = 17>8$. So, it can form a triangle.

Step3: Check 9 feet, 4 feet, 5 feet

$4 + 5=9$, which is not greater than 9. So, it cannot form a triangle.

Step4: Check 10 feet, 7 feet, 4 feet

$4 + 7 = 11>10$, $4+10 = 14>7$, $7 + 10=17>4$. So, it can form a triangle.

Step5: Check 12 feet, 5 feet, 6 feet

$5+6 = 11<12$. So, it cannot form a triangle.

Step6: Check 13 feet, 8 feet, 4 feet

$4 + 8=12<13$. So, it cannot form a triangle.

Answer:

8 feet, 7 feet, 10 feet; 10 feet, 7 feet, 4 feet