How many triangles exist with the given side lengths?
12 in, 15 in, 18 in
a) no triangle exists with the given side lengths.
b) exactly one unique triangle exists with the given side lengths.
c) more than one triangle exists with the given side lengths.

According to triangle inequality theorem, “The sum of the length of two sides of a triangle should be greater than the third side”. In order to verify the mentioned theorem, some calculations are performed below.

 12 + 15 > 18

15 + 18 > 12

12 + 18 > 15

As the triangle inequality theorem satisfied, so there is only one triangle possible with the given sides length. No more than one triangle is possible, because the angles are not given, and the sides length are fixed.

So option “B” is correct. 

26?

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.