In Exercises 15-22, determine whether the segment
lengths form a triangle. If so, is the triangle acute, right,
or obtuse? (See Example 5.)
15. 10,11 , and 14
16. 6,8 , and 14
17. 12,16 , and 20
18. 15,20 , and 26
19. , and 12.4
20. , and 7.8
21. 24,30 , and
22. 10,15 , and

Ask by Nichols Ayala. in the United States

Mar 25,2025

Question

In Exercises 15-22, determine whether the segment
lengths form a triangle. If so, is the triangle acute, right,
or obtuse? (See Example 5.)
15. 10,11 , and 14
16. 6,8 , and 14
17. 12,16 , and 20
18. 15,20 , and 26
19. , and 12.4
20. , and 7.8
21. 24,30 , and
22. 10,15 , and

Ask by Nichols Ayala. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

**15. Sides: 10, 11, 14** - Sort the sides: $$ a=10 $$, $$ b=11 $$, $$ c=14 $$. - Check the triangle inequality: $$ a+b=10+11=21>14=c. $$ - Since the triangle exists, we compare: $$ a^2+b^2=10^2+11^2=100+121=221, \quad c^2=14^2=196. $$ - Because $$ 221>196 $$, the triangle is acute. --- **16. Sides: 6, 8, 14** - Sort the sides: $$ a=6 $$, $$ b=8 $$, $$ c=14 $$. - Check the triangle inequality: $$ a+b=6+8=14 \not> 14=c. $$ - Since the sum equals the third side, these segments do not form a triangle. --- **17. Sides: 12, 16, 20** - Sort the sides: $$ a=12 $$, $$ b=16 $$, $$ c=20 $$. - Check the triangle inequality: $$ a+b=12+16=28>20=c. $$ - Compare the squares: $$ a^2+b^2=12^2+16^2=144+256=400, \quad c^2=20^2=400. $$ - Since $$ a^2+b^2=c^2 $$, the triangle is right. --- **18. Sides: 15, 20, 26** - Sort the sides: $$ a=15 $$, $$ b=20 $$, $$ c=26 $$. - Check the triangle inequality: $$ a+b=15+20=35>26=c. $$ - Compare the squares: $$ a^2+b^2=15^2+20^2=225+400=625, \quad c^2=26^2=676. $$ - Since $$ 625<676 $$, the triangle is obtuse. --- **19. Sides: $$4.1$$, $$8.2$$, $$12.4$$** - Sort the sides: $$ a=4.1 $$, $$ b=8.2 $$, $$ c=12.4 $$. - Check the triangle inequality: $$ a+b=4.1+8.2=12.3<12.4=c. $$ - Since the sum is less than the largest side, these segments do not form a triangle. --- **20. Sides: $$5.3$$, $$6.7$$, $$7.8$$** - Sort the sides: $$ a=5.3 $$, $$ b=6.7 $$, $$ c=7.8 $$. - Check the triangle inequality: $$ a+b=5.3+6.7=12.0>7.8=c. $$ - Compute the squares: $$ a^2\approx5.3^2=28.09,\quad b^2\approx6.7^2=44.89,\quad c^2\approx7.8^2=60.84. $$ - Then: $$ a^2+b^2\approx28.09+44.89=72.98>60.84=c^2. $$ - Since $$ a^2+b^2>c^2 $$, the triangle is acute. --- **21. Sides: 24, 30, $$6\sqrt{43}$$** - Identify the sides: $$ a=24 $$, $$ b=30 $$, $$ c=6\sqrt{43} $$. (Note: $$ 6\sqrt{43}\approx39.34 $$, so it is the largest side.) - Check the triangle inequality: $$ a+b=24+30=54>6\sqrt{43}\approx39.34. $$ - Compute the squares: $$ a^2+b^2=24^2+30^2=576+900=1476, $$ $$ c^2=(6\sqrt{43})^2=36\cdot43=1548. $$ - Since $$ 1476<1548 $$, the triangle is obtuse. --- **22. Sides: 10, 15, $$5\sqrt{13}$$** - Sort the sides: $$ a=10 $$, $$ b=15 $$, $$ c=5\sqrt{13} $$. (Note: $$5\sqrt{13}\approx18.03$$, so it is the largest side.) - Check the triangle inequality: $$ a+b=10+15=25>5\sqrt{13}\approx18.03. $$ - Compute the squares: $$ a^2+b^2=10^2+15^2=100+225=325, $$ $$ c^2=(5\sqrt{13})^2=25\cdot13=325. $$ - Since $$ a^2+b^2=c^2 $$, the triangle is right. **15. 10, 11, 14** Triangle is acute. **16. 6, 8, 14** Segments do not form a triangle. **17. 12, 16, 20** Triangle is right. **18. 15, 20, 26** Triangle is obtuse. **19. 4.1, 8.2, 12.4** Segments do not form a triangle. **20. 5.3, 6.7, 7.8** Triangle is acute. **21. 24, 30, 6√43** Triangle is obtuse. **22. 10, 15, 5√13** Triangle is right.

In Exercises 15-22, determine whether the segment
lengths form a triangle. If so, is the triangle acute, right,
or obtuse? (See Example 5.)
15. 10,11 , and 14
16. 6,8 , and 14
17. 12,16 , and 20
18. 15,20 , and 26
19. , and 12.4
20. , and 7.8
21. 24,30 , and
22. 10,15 , and

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In Exercises 15-22, determine whether the segment lengths form a triangle. If so, is the triangle acute, right, or obtuse? (See Example 5.) 15. 10,11 , and 14 16. 6,8 , and 14 17. 12,16 , and 20 18. 15,20 , and 26 19. , and 12.4 20. , and 7.8 21. 24,30 , and 22. 10,15 , and

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Related Questions

Latest Geometry Questions

In Exercises 15-22, determine whether the segment
lengths form a triangle. If so, is the triangle acute, right,
or obtuse? (See Example 5.)
15. 10,11 , and 14
16. 6,8 , and 14
17. 12,16 , and 20
18. 15,20 , and 26
19. , and 12.4
20. , and 7.8
21. 24,30 , and
22. 10,15 , and