98
1. what is the value of x?
2.what is the value of x?
3.what is the value of x?

Look at the picture.

If ABC is any triangle and AD bisects (cuts in half) the angle BAC, then

1. In our triangle we have the proportion:

We have

AD = 2.25, AC = 3, BC = 4, BD = x.

Substitute:

       multiply both sides by 4

2. In our triangle we have the proportion:

We have

BD = x + 4, BA = 8, CD = 2x + 1, CA = 12.

Substitute:

             cross multiply

             use distributive property a(b + c) = ab + ac

         subtract 48 from both sides

              subtract 16x from both sides

             divide both sides by (-4)

3. We have the similar triangles (AAA). Therefore the lengths of the sides are in proportion:

          multiply both sides by 8

1. Set up a ratio: 3/2.25 = 4/x

Cross multiply:

3x = 2.25*4

3x = 9

Divide both sides by 3:

x = 9/3

x = 3

2. Set up a ratio: 12/2x+1 = 8/x+4

Cross multiply:

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

Simplify:

12x +48 = 16x +8

Subtract 8 from each side:

12x +40 = 16x

Subtract 12x from each side:

40 = 4x

Divide both sides by 4:

x = 40/4

X = 10

3. Find the ratio of the smaller triangle to the larger triangle: using the two ends: 15 /5 = 3

The larger triangle is 3 times larger than the smaller one.

Because the two given angles are on opposite sides, this means the sides of the triangle are mirrored so X is the equivalent of side 8 times the ratio:

x = 8 *3 = 24

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step-by-step explanation: