Question

leveled practice in 1-6, determine if the given side lengths could form a triangle.

1. 3 m, 4 m, 10 m

$3^{2}+4^{2}=10^{2}$
$9 + 16 = 100$
$25 \
eq 100$ no

1. 5 in., 6 in., 8 in.

$5^{2}+6^{2}=8^{2}$
$25 + 36 = 64$
$61 \
eq 64$ no

1. 4.5 cm, 6.8 cm, 5.2 cm

$4.5^{2}+6.8^{2}=5.2^{2}$
$20.25 + 46.24 = 27.04$

1. 0.7 ft, 3.3 ft, 1.4 ft
2. 13.6 mm, 17.1 mm, 20.4 mm
3. 0.2 yd, 0.7 yd, 0.5 yd

Explanation:

Step1: Recall triangle inequality rule

For side lengths $a, b, c$, the sum of any two sides must be greater than the third side: $a+b>c$, $a+c>b$, $b+c>a$.
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Step1 (Problem1): Test 3m,4m,10m

Check $3+4 > 10$: $7 > 10$ is false.

Step2 (Problem1): Conclusion for 1

Since one inequality fails, no triangle.
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Step1 (Problem2): Test 5in,6in,8in

Check $5+6>8$ ($11>8$ true), $5+8>6$ ($13>6$ true), $6+8>5$ ($14>5$ true).

Step2 (Problem2): Conclusion for 2

All inequalities hold, triangle forms.
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Step1 (Problem3): Test 4.5cm,6.8cm,5.2cm

Check $4.5+6.8>5.2$ ($11.3>5.2$ true), $4.5+5.2>6.8$ ($9.7>6.8$ true), $6.8+5.2>4.5$ ($12>4.5$ true).

Step2 (Problem3): Conclusion for 3

All inequalities hold, triangle forms.
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Step1 (Problem4): Test 0.7ft,3.3ft,1.4ft

Check $0.7+1.4 > 3.3$: $2.1 > 3.3$ is false.

Step2 (Problem4): Conclusion for 4

Since one inequality fails, no triangle.
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Step1 (Problem5): Test 13.6mm,17.1mm,20.4mm

Check $13.6+17.1>20.4$ ($30.7>20.4$ true), $13.6+20.4>17.1$ ($34>17.1$ true), $17.1+20.4>13.6$ ($37.5>13.6$ true).

Step2 (Problem5): Conclusion for 5

All inequalities hold, triangle forms.
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Step1 (Problem6): Test 0.2yd,0.7yd,0.5yd

Check $0.2+0.5 > 0.7$: $0.7 > 0.7$ is false (needs to be greater than, not equal).

Step2 (Problem6): Conclusion for 6

Since one inequality fails, no triangle.

Answer:

1. No
2. Yes
3. Yes
4. No
5. Yes
6. No