104k views
4 votes
In Square ABCD, AE = 3x + 5 and BD = 10x + 2.What is the length of AC?

In Square ABCD, AE = 3x + 5 and BD = 10x + 2.What is the length of AC?-example-1

1 Answer

2 votes

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}

User Esben Tind
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories