Question

if bc = 2x, cd = x + 2, and bd = 5, what is cd? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up equation

Since $BC + CD=BD$, we have $2x+(x + 2)=5$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $3x+2 = 5$.

Step3: Isolate the variable term

Subtract 2 from both sides: $3x=5 - 2$, so $3x=3$.

Step4: Solve for $x$

Divide both sides by 3: $x = 1$.

Step5: Find the value of $CD$

Substitute $x = 1$ into the expression for $CD$. Since $CD=x + 2$, then $CD=1+2=3$.

Answer:

3