Question

point d is on segment dc. segment bc measures 8x units in length. what is the length of segment bc? units c d b 3x + 8 4x + 10

Explanation:

Step1: Set up equation

Since $BC = CD + DB$ and $BC = 8x$, $CD=3x + 8$, $DB = 4x+10$, we have the equation $8x=(3x + 8)+(4x + 10)$.

Step2: Simplify right - hand side

Combine like terms on the right - hand side: $(3x + 8)+(4x + 10)=3x+4x + 8 + 10=7x + 18$. So the equation becomes $8x=7x + 18$.

Step3: Solve for x

Subtract $7x$ from both sides of the equation: $8x-7x=7x + 18-7x$. This gives $x = 18$.

Step4: Find length of BC

Substitute $x = 18$ into the expression for $BC$ (which is $8x$). So $BC=8\times18 = 144$.

Answer:

144