Your teacher made 8 triangles he need help to identify what type triangles they are. Help him?:
1) #12, 16, 20#
2) #15, 17, 22#
3) #6, 16, 26#
4) #12, 12, 15#
5) #5,12,13#
6) #7,24,25#
7) #8,15,17#
8) #9,40,41#

Question

Let's say your teacher told you that he made the 8 triangles but he does not know what type triangles they are. Can you help him identify what type of triangles she made:
1) #12, 16, 20#
2) #15, 17, 22#
3) #6, 16, 26#
4) #12, 12, 15#
5) #5,12,13#
6) #7,24,25#
7) #8,15,17#
8) #9,40,41#

Violet Aldrich · Accepted Answer

According to Pythagoras theorem    we have the following relation for a right angled triangle. #"hypotenuse"^2= "sum of square of other smaller sides"# This relation holds good for
triangles #1,5,6,7,8->"Right angled"#
They are also Scalene Triangle as their  three sides are unequal in length. #(1)->12^2+16^2=144+256=400=20^2# #(5)->5^2+12^2=25+144=169=13^2# #(6)->7^2+24^2=49+576=625=25^2# #(7)->8^2+15^2=64+225=289=17^2# #(8)->9^2+40^2=81+1600=1681=41^2#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#(3)->6+16<26->"Triangle not possible"# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #(2)->15!=17!=22->"Scalene triangle"# #(4)->12=12!=15->"Isosceles triangle"#

Sadie Allen · Answer

1) #12,16,20#: Scalene, right triangle
2) #15,17,22#: Scalene
3) #6,16,26#: Triangle does not exist.
4) #12,12,15#: Isosceles
5) #5,12,13#: Scalene, right triangle
6) #7,24,25#: Scalene, right triangle
7) #8,15,17#: Scalene, right triangle
8) #9,40,41#: Scalene, right triangle

From a theorem we know that
The sum of the lengths of any two sides of a triangle must be greater than the third side. If this is not true, triangle does not exist.
We test the given set of values in each instance and notice that in case of
3) #6,16,26# the condition is not met as
#6+16 # is not# > 26#.

To identify different types of triangles either by way of given lengths of its sides or measure of its three angles is shown below:

In the problem three sides of each triangle are given. As such we will identify these by sides.

1) #12,16,20#: All three sides are of unequal lengths, therefore Scalene
2) #15,17,22#: All three sides are of unequal lengths, therefore Scalene
3) #6,16,26#: Triangle does not exist.
4) #12,12,15#: Two sides are of equal lengths, therefore Isosceles
5) #5,12,13#: All three sides are of unequal lengths, therefore Scalene
6) #7,24,25#: All three sides are of unequal lengths, therefore Scalene
7) #8,15,17#: All three sides are of unequal lengths, therefore Scalene
8) #9,40,41#: All three sides are of unequal lengths, therefore Scalene

There is a fourth category of triangles in which one of interior angles is of #90^@#.
It is called right triangle.

Jayden Jackson · Answer

undefined Sure, I can help identify the type of triangles:

1) Right triangle (Pythagorean triple)
2) Scalene triangle
3) Scalene triangle
4) Isosceles triangle
5) Right triangle (Pythagorean triple)
6) Scalene triangle
7) Right triangle (Pythagorean triple)
8) Right triangle (Pythagorean triple)

Your teacher made 8 triangles he need help to identify what type triangles they are. Help him?: 1) #12, 16, 20# 2) #15, 17, 22# 3) #6, 16, 26# 4) #12, 12, 15# 5) #5,12,13# 6) #7,24,25# 7) #8,15,17# 8) #9,40,41#

Let's say your teacher told you that he made the 8 triangles but he does not know what type triangles they are. Can you help him identify what type of triangles she made: 1) #12, 16, 20# 2) #15, 17, 22# 3) #6, 16, 26# 4) #12, 12, 15# 5) #5,12,13# 6) #7,24,25# 7) #8,15,17# 8) #9,40,41#

Let's say your teacher told you that he made the 8 triangles but he does not know what type triangles they are. Can you help him identify what type of triangles she made:
1) #12, 16, 20#
2) #15, 17, 22#
3) #6, 16, 26#
4) #12, 12, 15#
5) #5,12,13#
6) #7,24,25#
7) #8,15,17#
8) #9,40,41#