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 leng
th of the side of the rhombus if AB=c, and AC=b.
1 answer:
Answer:
The length of the rhombus is =
Step-by-step explanation:
It is given that the 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:
⇒
⇒
Now, ΔDBE is similar to ΔABC, then
DE=
=
=
Thus, the length of the rhombus is =
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Answer:
Attached diagram A'B'C'D'
Step-by-step explanation:
Given is a quadrilateral ABCD. It says to draw a dilated version with a scale factor 2/3.
We see that scale factor is less than 1 which means it shrinks the image to a smaller one.
To draw a scaled copy, we need to find the lengths of its sides.
To do so, we can draw the diagonals AC & BD, and they intersect at origin O(0,0) such that OA= -2, OB= 2, OC= 4, OD= -4.
Applying a scale factor of 2/3, we get OA' = -4/3, OB' = 4/3, OC' = 8/3, OD' = -8/3.
So we have attached a scaled copy A'B'C'D' of quadrilateral ABCD with a scale factor 2/3.
For this case, the full length of the log is equal to 1.
Therefore, the remaining length, we can obtain it by means of the following expression:
Rewriting we have:
Then, subtracting both numbers we have:
Answer:
The remaining amount of log is given by: