Question

C is the centroid of triangle RST. Find the length indicated using the given information. SC =5x-16 and SO=7x-17.

Answer 1

Step-by-step explanation:

The centroid of a triangle divides the median from the other vertices in the ratio 2:1.

So,

SC : OC = 2:1

SC = 2OC70

Given SC = 5x - 16

SO = 7x -17

But SO = SC + OC

This implies OC = SO - SC = 7x-17-5x+16 = 2x - 1

So SC : OC = 5x - 16: 2x-1 = 2:1

Setting an equation:(Solve for x:)

$\dfrac{5x - 16}{2x - 1} = \dfrac{2}{1}$

Multiply both sides by (2x - 1):

• 5x - 16 = 2(2x-1) [On LHS,(2x - 1) cancels]

Apply Distributive property to RHS:

• 5x - 16 = 4x - 2

Subtract 4x from both sides:

• 5x-4x - 16 = -2
• x -16 = -2

Add 16 to both sides:

• x = -2 + 16 = 14

Hence the size of x = 14 units

The size of CO = 2*x -1 = 2*14-1 = 28-1 = 27 units