Question

The figure below shows rectangle ABCD and triangle ECA on a coordinate plane which of the following expressions represents the perimeter of triangle ECA in units

Answer 1

The Solution:

Given:

Required:

To find the perimeter of the triangle ECA.

By the Pythagorean Theorem,

$\begin{gathered} 10^2+4^2=CA^2 \\ 100+16=CA^2 \\ CA^2=116 \end{gathered}$$|CA|=\sqrt{116}^=2\sqrt{29}$

Step 2:

Find the length of AE.

$|AE|=\sqrt{(-8-6)^2+(-9--1)^2}=2\sqrt{65}$

step 3:

Find EC.

$\lvert EC\rvert=\sqrt{(4--8)^2+(3--9)^2}=12\sqrt{2}$

So, the required perimeter is:

$P=(2\sqrt{29}+2\sqrt{65}+12\sqrt{2})$