Question

In Square ABCD, AE = 3x + 5 and BD = 10x + 2.What is the length of AC?

Answer 1

Let's begin by identifying key information given to us:

We have square ABCD

`\begin{gathered} AE=3x+5 \\ BD=10x+2 \\ BD=2\cdot AE \\ 10x+2=2(3x+5) \\ 10x+2=6x+10 \\ \text{Put like terms together, we have:} \\ 10x-6x=10-2 \\ 4x=8 \\ \text{Divide both sides by ''4'', we have:} \\ (4x)/(4)=(8)/(4) \\ x=2 \\ \\ \end{gathered}`

For a square, the diagonals are equal, AC = BD

`\begin{gathered} AC=BD \\ AC=10x+2 \\ x=2 \\ AC=10(2)+2=20+2 \\ AC=22 \end{gathered}`