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I need help with this problem

User Anudeep
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Answer: x = 4

We are given two similar triangles

CB = XP

AB = RP

CB = 8

XP = 12

AB = 6

RP = 2x + 1

Using similarity triangle theorem


\begin{gathered} (CB)/(XP)\text{ = }(AB)/(RP) \\ (8)/(12)\text{ = }\frac{6}{2x\text{ + 1}} \\ \text{Collect the like terms} \\ 12\text{ x 6 = 8(2x + 1)} \\ \text{Open the parenthesis} \\ 72\text{ = 16x + 8} \\ 16x\text{ = 72 - 8} \\ 16x\text{ = 64} \\ \text{Divide both sides by 16} \\ (16x)/(16)\text{ = }(64)/(16) \\ x\text{ = 4} \end{gathered}

User Panayiotis Irakleous
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