Jon G. answered • 03/26/21
HS Geometry teacher College/GED tutor > 10 years experience
Hi Jesus...I am Jon...
I will help you begin to learn to use what I am presuming your teacher has already helped you with, as far as the information give to you. I will tell you up from, that I will not answer the problem for you. As a teacher, I help students learn to make sure you understand what the problem is asking of you, then offer you some guidance in working toward a solution. I can certainly answer the problem, but I believe that will not help you, if a similar problem is on a quiz or test, I am no there to help you. If I can help you look at a problem then, think about how to 'problem-solve' then what I've helped you with, you take that with you into a test. So...let's begin...
You are given a problem, that is asking you to use a concept...the Pythagorean Theorem, as a tool to help in solving this problem. Let's being with looking at what we have with the information you've been given.
Given: AC ⊥ DB This tells you that the lines AC and DB for the 4 right angles
∠ DEC, ∠ DEA, ∠ BEC, & ∠BEA
From this you polygon meets the requirements of using the Pythagorean Theorem.
And because of this information you are able to use the a2 + b2 = c2
From the polygon, it also states that lines DE and BE are equal because of the 2 marks
on each of the lines.
The information from the polygon also then states that line DE is 12 cm in length.
From this information, you can prove and determine the lengths of line DE and BE.
Since they equal lengths, bisected by line AC and the the entire length of DB is 12 cm,
then by bisecting it, basically cutting it in half, then line DE is 6 cm and line BE is 6 cm.
With this information, let's take one triangle, Δ DEA
On Δ DEA you have one side of Δ DEA as line DA, which is the hypotenuse, measuring 7 cm.
From the information above, you have reasoned and determined that on Δ DEA line DE is
6 cm in length.
Now let's but that into the Pythagorean Theorem: a2 + b2 = c2
But we have use the information associated the the lines you are give.
line (a) is DE which is 6 cm
line (b) is EA we don't know this value, this is the one we have to calculate
line (c) is DA or the hypotenuse which is 7 cm
Substitute it into the Pythagorean Theorem
(DE)2 + (EA)2 = (DA)2
Continue to substitute:
62 cm + (EA)2 cm = 72 cm
Make your calculations:
36 cm2 + (EA)2 cm = 49 cm2
Now you can solve for EA
36 cm2 - 36 cm2 + (EA)2 = 49 cm2 - 36 cm2
and so
(EA)2 = 13 cm2
solve for EA with the square root
√(EA)2 = √13 cm2
Solve for the square root of 13 cm2
which is EA = 3.606 cm or to the nearest tenth 3.6 cm
That is how you begin to solve these kinds of problems...follow the rest of the examples and good luck
I am here to help if you need assistance.
Jon
