Question

HELP PLZ GEOMETRY - 50 POINTS

What is value of x?



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x =

Answer 1

x = 10.

Explanation:

We can prove quite easily that the two triangles are similar.

So comparing the ratio of the sides give us: 8/12 = (x + 4)/(2x + 1).

Simplifying the equation gives us:

2/3 = (x + 4)/(2x + 1)

3(x + 4) = 2(2x + 1)

3x + 12 = 4x + 2

x = 10.

Answer 2

x=10

Explanation:

We can use Triangle angle bisector theorem and proportions to solve this problem. We put the small triangle side over the large triangle side

8 x+4

------ = ------------

12 2x+1

Using cross products

8(2x+1) = 12(x+4)

16x+8 =12x+48

Subtract 12x from each side

16x-12x +8 = 12x-12x+48

4x+8 = 48

Subtract 8 from each side

4x+8-8 = 48-8

4x = 40

Divide by 4

4x/4 = 40/4

x = 10