In ^DEF, the bisector of <F divides the opposite sides into segments that are 4 and 9in long. The side of the triangle adjacent to the 4 in. segment is 6in long. To the nearest tenth of an inch, how long is the third side of the triangle?
If the other side is x,
x/6 = 9/4
I guess you can figure x from that ok?
how do you round 9.84 to the nearest tenth of a unit
To find the length of the third side of the triangle, we can apply the angle bisector theorem. The angle bisector theorem states that if a line bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides.
Let the length of the third side of the triangle be "x" inches.
According to the angle bisector theorem, we can set up the following proportion:
(Length of segment adjacent to the 4 in. segment) / (Length of segment adjacent to the 9 in. segment) = (Length of the 4 in. segment) / (Length of the 9 in. segment)
Therefore, we have:
6 / x = 4 / 9
Cross-multiplying, we get:
4x = 6 * 9
4x = 54
Dividing both sides by 4, we get:
x = 54 / 4
x = 13.5
Therefore, the third side of the triangle is approximately 13.5 inches long.
To find the length of the third side of the triangle, we can use the Angle Bisector Theorem. According to this theorem, the length of a segment formed by an angle bisector divides the opposite side into segments that are proportional to the adjacent sides of the triangle.
Let's denote the length of the third side of the triangle as "x". We know that the side adjacent to the 4 in. segment has a length of 6 in. Therefore, we have the following relationship:
4 / 9 = 6 / x
To find x, let's cross-multiply and solve for it:
4x = 9 * 6
4x = 54
x = 54 / 4
x = 13.5
Therefore, the length of the third side of the triangle is approximately 13.5 inches.