The lengths of the sides of the triangle are 2/3 the lengths of the sides of a similar triangle, if the side of the larger triangle is 36 millimeters, what is the measure of the matching side of the smaller triangle?

The matching side of the smaller triangle measures 24 millimeters.

Step-by-step explanation: From the details given, both triangles are similar by virtue of the measurement of their sides, that is, SSS. Also the smaller triangle measures two-thirds of the larger triangle.

What this means is that every time we measure the larger triangle, for example as X millimeters, we can scale it down to the smaller one by using the two-thirds ratio of similarity. In other words, if the larger one measures 36 mm, then the smaller one would measure;

A = 36 x (2/3)

A = 24

Therefore the measure of the matching side of the smaller triangle equals 24 millimeters

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.