Answer:
Step-by-step explanation:
When two triangles are similar, it means that the ratio of their corresponding sides is equal.
Therefore
96/(6x + 28) = 24/25
Crossmultiplying,
1) 96 × 25 = 24(6x + 28)
2400 = 144x + 672
144x = 2400 - 672 = 1728
x = 1728/144
x = 12
2) angle A and angle D is equal because they are alternate angles.
(2x + 6)/(x + 6) = 10/8
Crossmultiplying
8(2x + 6) = 10(x + 6)
16x + 48 = 10x + 60
16x - 10x = 60 - 48
6x = 12
x = 12/6 = 2
3) both triangles are right angle triangles. All angles are similar in both triangles. It also means that all the sides are similar. Therefore
45/30 = 40/x
Crossmultiplying
45 × x = 30 × 40
45x = 120
x = 120/45 = 26.7
