12) Two rectangles are similar. The length of small rectangle is 4 and the length of the big rectangle is 12. If the perimeter of the smaller rectangle is 28, then what is the perimeter
of the larger rectangle

84

Step-by-step explanation:

To get from 4 to 12, you multiply with 3.

Everything is 3 times as big in the larger rectangle.

This includes the perimeter.

Example:

small rect 4x10, perimeter 4+4+10+10 = 28

large rect 12x30, perimeter 12+12+30+30 = 84

but also 28x3 = 84

b||c; c||d; b||d

Step-by-step explanation:

Substituting 10 for x, in the angle beside b we have

7(10)-5 = 70-5 = 65

In the angle beside c we have

10(10)+15 = 100+15 = 115

In the angle beside d we have

12(10)-5 = 120-5 = 115

In the angle beside we have

8(10)-25 = 80-25 = 55

The angle beside c has a vertical angle on the other side of c.  This angle would be same-side interior angles with the angle beside b; this is because they are inside the block of lines made by b and c and on the same side of a, the transversal.  These two angles are supplementary; this is because 65+115 = 180.  Since these angles are supplementary, this means that b||c.

The angle beside c and the angle beside d would be alternate interior angles; this is because they are inside the block of lines made by c and d and on opposite sides of the transversal.  These two angles are congruent; this means that c||d.

Since b||c and c||d, by the transitive property, b||d.