Answer with Step-by-step explanation:
We have to find given length set form a triangle and find the type of triangle acute, obtuse or right.
If sum of length of any two sides is greater than the length of third side then the given side length form a triangle otherwise not.
a.5 cm, 6 cm and 7 cm
[tex]5+6=11cm > 7cm[/tex]
Hence, given set of side length form a triangle.
[tex]5^2+6^2=25+36=61 >7^2=49[/tex]
Hence, given triangle is acute triangle.
b.2 cm,11 cm,15 cm
[tex] 2+15=17 cm > 11 cm[/tex]
Hence, given side length set form a triangle.
[tex]2^2+11^2=4+121=125 < (15)^2=225[/tex]
Hence, the triangle is an obtuse triangle.
c.10 cm,15 cm,20 cm
[tex]10+15=25 cm >20 cm[/tex]
Hence, given set of length side form a triangle.
[tex](10)^2+(15)^2=225 >(20)^2=400[/tex]
Hence, the triangle is an acute triangle .
d.10 cm,24 cm,26 cm
[tex]10+24=34 cm > 26 cm[/tex]
Hence, given set of side length form a triangle.
[tex](10)^2+(24)^2=676=(26)^2=676[/tex]
Hence, the triangle forms a right triangle.
e.1 cm,3 cm, 9 cm
[tex]1+9=10 cm > 3 cm[/tex]
Hence, the given set of side length forms a triangle.
[tex]1^1+3^2=10<9^2=81[/tex]
Hence, the triangle is an obtuse triangle.
f.2 cm, 10 cm,11 cm
[tex]2+10=12 cm > 11cm[/tex]
Hence, the given set of side length set forms a triangle.
[tex]2^2+(10)^2=104<(11)^2=121[/tex]
Hence, the triangle is an obtuse triangle.
