# Geometry

posted by .

One side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3-inch and 5-inch segments. Find the perimeter of the triangle in terms of x. ( triangle angle bisector theorem)

• Geometry -

let the shorter side be a, then the longer side is a+x
by the Triangle Angle Bisector Theorm

(a+x)/5 = a/3
3a + 3x = 5a
3x = 2a
a = 3x/2 = 1.5x

so the sum of the three sides
= a + a+x + 8
= 1.5x + x + 8
= 2.5x + 8

• Geometry -

Reiny, if a+a+x+8 then how come it is 1.5x+x+8=2.5x+8? I thought that it is 1.5x+1.5x+x+8=4x+8. Previous problem:one side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3-inch and 5-inch segments. Find the perimeter of the triangle in terms of x.

• Geometry -

Anonymous is correct, for the answer is 4x+8.

## Similar Questions

1. ### geometry

A triangle has a 56-degree angle, formed by a 10-inch side and an x-inch side. Given that the area of the triangle is 18 square inches, find x.
2. ### Trig

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (a) Find the area of triangle PQR. (b) Find the length of the projection of segment PQ onto segment PR. (c) Find the length …
3. ### math pls

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (d) Find the sizes of the other two angles of triangle PQR. (e) Find the length of the median drawn to side PQ. (f) Find …
4. ### geometry/math pls help

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (1) Find the sizes of the other two angles of triangle PQR. (2) Find the length of the median drawn to side PQ. (3) Find …
5. ### Geometry

Reiny, according to this problem(one side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3-inch and 5-inch segments. Find the perimeter of the triangle …
6. ### Geometry

One side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3- inch and 5-inch segments. Find the perimeter of the triangle in terms of x.
7. ### Geometry

One side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3-inch and 5-inch segments. Find the perimeter of the triangle in terms of x. ( triangle …
8. ### geometry

An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle. …
9. ### Geometry

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 …
10. ### geometry (check answers)

Determine whether you can construct many, one, or no triangle(s) with the given description. a) a triangle with angle measures of 50°, 70°, and 100° no b) a triangle with one angle measure of 60° and one 4-centimeter side no c) …

More Similar Questions