g is the centroid of triangle abc\nwhat is the value of x?\nwhat is the length of segment dg? units\nwhat is…

g is the centroid of triangle abc\nwhat is the value of x?\nwhat is the length of segment dg? units\nwhat is the length of segment ag? units\nwhat is the length of segment ad? units

g is the centroid of triangle abc\nwhat is the value of x?\nwhat is the length of segment dg? units\nwhat is the length of segment ag? units\nwhat is the length of segment ad? units

Answer

Answer:

  • (x = 22)
  • Length of segment (DG=7) units
  • Length of segment (AG = 29) units
  • Length of segment (AD=36) units

Explanation:

Step1: Use centroid property

The centroid (G) divides each median in a ratio (AG:GD = 2:1). So (AG = 2GD). Given (AG=x + 7) and (GD=x-15). Then (x + 7=2(x - 15)).

Step2: Solve for (x)

Expand the right - hand side: (x+7 = 2x-30). Subtract (x) from both sides: (7=2x - 30-x). Simplify: (x=30 + 7=22).

Step3: Find length of (DG)

Substitute (x = 22) into (DG=x - 15). So (DG=22-15 = 7) units.

Step4: Find length of (AG)

Substitute (x = 22) into (AG=x + 7). So (AG=22+7=29) units.

Step5: Find length of (AD)

Since (AD=AG + GD), and (AG = 29) units, (GD = 7) units. Then (AD=29+7=36) units.