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|=√(116)^=2√(29)`

Step 2:

Find the length of AE.

`|AE|=√((-8-6)^2+(-9--1)^2)=2√(65)`

step 3:

Find EC.

`\lvert EC\rvert=√((4--8)^2+(3--9)^2)=12√(2)`

So, the required perimeter is:

`P=(2√(29)+2√(65)+12√(2))`