Given that triangle DAE ~ triangle BAC, what is the length of side AE?
1 answer:
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Answer: 96
Step-by-step explanation:
Ok, lines a and b are parallel.
We can separate this problem in two cases:
Case 1: 2 vertex in line a, and one vertex in line b.
Here we use the relation:
"In a group of N elements, the total combinations of sets of K elements is given by"
Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.
Then if we have two vertices in line a, we have:
N = 6, K = 2
And the other vertex can be on any of the four points on the line b, so the total number of triangles is:
C = 15*4 = 60.
But we still have the case 2, where we have 2 vertices on line b, and one on line a.
First, the combination for the two vertices in line b is:
We use N = 4 and K = 2.
And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:
C = 6*6 = 36
Then, putting together the two cases, we have a total of:
60 + 36 = 96 different triangles
Answer:
(a) 4+5i or, 4-3i
(b) 1+6i
Step-by-step explanation:
The distance between the points A= 1+i, and B=a+bi is 5.
Therefore, we can write
⇒ ..... (1)
(a) If the value of a is 4, then from equation (1), we get
(4-1)²+(b-1)² = 25
⇒ (b-1)² =16
⇒ b-1 =±4
⇒ b= 5 or -3
Therefore, the point B will be represented by 4+5i or, 4-3i (Answer)
(b) If the value of b is 6, then from equation (1), we get
(a-1)²+(6-1)² = 25
⇒ (a-1)² =0
⇒ a = 1
Therefore, the point B will be represented by 1+6i. (Answer)