rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side
bc
. what is the length of the side of the rhombus if ab=c, and ac=b.

Step-by-step explanation:

Given that Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC.Then,

AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:

⇒

⇒

Also, ΔDBE is similar to ΔABC, then

=

Therefore, the length of the rhombus is =

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: