The height of the trunk is 26 inches the length of the trunk is 50 inches. The tv is 54 inches wide. And 96 inches in height Use the Pythagorean theorem to calculate the length of the diagonal of the trunk.

The length of the diagonal of the trunk is 56.356011 inches

Step-by-step explanation:

According to the given data we have the following:

height of the trunk= 26 inches

length of the trunk= 50 inches

According to the Pythagorean theorem, to calculate the length of the diagonal of the trunk we would have to calculate the following formula:

length of the diagonal of the trunk=√(height of the trunk∧2+length of the trunk∧2)

Therefore, length of the diagonal of the trunk=√(26∧2+50∧2)

length of the diagonal of the trunk=√3176

length of the diagonal of the trunk=56.356011

The length of the diagonal of the trunk is 56.356011 inches

 The center of dilation is the origin (0, 0) and scale factor is 3.

Step-by-step explanation:  We are given to describe a dilation that that transforms ΔRST to ΔR'S'T', or to explain why it cannot be done.

We can see in the figure provided that both the triangles are right-angles at angles S and S'

Also, RS = ST = 1 unit   and   R'S' = S'T' = 3 units.

Using Pythagoras theorem, we have

and

Therefore, the ratio of the corresponding sides will be

Since the ratio of the corresponding sides are equal, so the two triangles are similar.

Hence, ΔRST can be dilated to form ΔR'S'T'.

The center of dilation will be origin (0, 0), because the shapes of the two triangles are same with respect to the origin.

Also, since the ratio of any two corresponding sides of the triangles is 3, so the scale factor is 3.

Thus, ΔRST can be dilated to ΔR'S'T' with origin (0, 0) as the center of dilation and scale factor 3.