Question

ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°,m∠APB=12y°, and ∠m∠ACP= (4y - 1)°.CD = __ .

Answer 1

Given: A rhombus ABCD

`\begin{gathered} AB=2x+12 \\ AC=7x-3 \\ m\angle APB=12y^0 \\ m\angle ACP=(4y-1)^0 \end{gathered}`

To Determine: The CD

Solution

Please note that the four sides of a rhombus are the same side lengths

`\begin{gathered} AB=AC=CD=BD \\ Therefore \\ AB=AC \\ 2x+12=7x-3 \\ 2x-7x=-3-12 \\ -5x=-15 \\ (-5x)/(-5)=(-15)/(-5) \\ x=3 \end{gathered}`
`\begin{gathered} AB=2x+12 \\ AB=2(3)+12 \\ AB=6+12 \\ AB=18 \end{gathered}`

Since all the side lengths of the rhombus are the same, then CD = 18 units