NMOS 2023 R2 Q10 - Perimeter Problem

Hello everyone, I am Tjen from Kangru study and welcome back to our YouTube channel again. Now in this video we are

channel again. Now in this video we are going to discuss this geometry question from UNMOS 2023. So in this question we have to find out a clever method in

order to solve the parameter of an irregular shape. So without further ado

irregular shape. So without further ado it let us take a look at the question together.

Now in this question it says the diagram below shows a pendon A B CDE E such that

AB is 10 cm AE is 7 cm. Now CD is 3 cm and the angle ABC BCD CDE E and D8. So

all these angles indicated in the figure they are all 120°. So they want us to find the parameter of the pentagon A B C D itself.

Now looking at the question in order to get a parameter of course we had to know the length of all the lines here. So we

already know three of them this 7 cm 10 cm and 3 cm. But how about DE and BC? So

of course we cannot solve the question directly because these are not given to us. Then how else can we solve the

us. Then how else can we solve the question? So everyone we are going to

question? So everyone we are going to notice there is one condition we haven't used yet. Which one is it? And we going

used yet. Which one is it? And we going to see that this will be the 120° angle here. Now let's think what's

so special about the angle 120. Now of

course these angles given to us there must be a meaning to it. So we going to see that for 120° angle of course this

one itself is not so special but the supplementary angle of 120 is what that will be 60°.

And if we draw the straight line here now we're going to see that this angle will be 60°. So the 120° is what we call

the interior angle of the pentagon. Of

course the 60° angle is what we call the exterior angle of the pentagon. So

exterior angle this is 60. Now does this angle ring a bell here.

So we are going to see right where do we observe 60° angle. Oh so this will be in equilateral triangle. So let's see for

equilateral triangle. So let's see for the other 120° angle. If we do the same let's extend the line here. Hey we going

to see the exterior angle is also 60° 180 minus 120. So 60 60 and we form a triangle here. Now everyone what is the

triangle here. Now everyone what is the third angle? So this will be 60° as

third angle? So this will be 60° as well. So at this corner actually we have

well. So at this corner actually we have found a equilateral triangle. So of

course for the other side right at the corner of B and C we can just do the same. So here extend the line AB we can

same. So here extend the line AB we can find out that this angle is 60°. Extend

the line DC. So this angle is also 60°.

So 60 60. The last angle is also 60 within the triangle itself.

So now from the figure actually what we can find is now we have one equilateral triangle at the bottom left corner another equilateral triangle at the

bottom right corner. So after knowing this let's label the two points here let's call them F and G. Now what else can we find from the figure? So what we

can see is that in the equilateral triangle itself all three sides will be of the same length. So let's label them

here. Suppose we call D to be A then E F

here. Suppose we call D to be A then E F and DF will also be A. So for the other triangle let's say we call BC is B. Then

this means that BG and CG will also be B.

So knowing this how does that help us to solve the equation? So we have the equilateral triangles but still we cannot find the A and B directly.

So of course we have to jump out of the box here everyone only looking at these two is not enough to solve the question.

Now what other triangle can we look at?

So we're going to see that this is 60 60 and for the bigger triangle EFG what kind of triangle is this? So this will

also be an equal triangle where all three angles are 60°.

So knowing the triangle AFG is equilateral. How does that help us? Ahuh

equilateral. How does that help us? Ahuh

we are going to see that the three lines will be the same. So AF, FG and AG they are of the same length. So let's

indicate each of them clearly. For AF

this will be A + 7. Then for FG this will be A + B + 3 C. Then for AG we will get 10 + B.

So level what we have just said three of them they are of the same length. So

let's make the comparison here. Now

suppose we compare the first two fg and af these two are equal to each other. So

fg is a + b + 3 and af is a + 7. Now can

we simplify the equation right? So we're

going to see on both sides we have the number a. Of course we can cancel the

number a. Of course we can cancel the same number from the two sides. So

cancel the eight a do we have b + 3 = to 7. Then what is b? So b will be 7 - 3 b

7. Then what is b? So b will be 7 - 3 b = 4. Now comparing the first two we can

= 4. Now comparing the first two we can figure out the value of b. Then now we still have to find the value of a. So of

course we will try to cancel out the other unknown t. So that's why we select the two equations where both of them contain the letter B here. So now

compare between FG and AG. So they are equal to each other. Now FG is A + B + 3. A G is B + 10. What can we cancel

3. A G is B + 10. What can we cancel everyone? So we can cancel the same

everyone? So we can cancel the same letter which is the letter B. So cancel

out the B we get a + 3 = to 10. And what

is A? So a will be 10 - 3 this will be 7. Now knowing that b = to 4 and a = to

7. Now knowing that b = to 4 and a = to 7 are we able to find the parameter of the pentagon? Of course we can. So we

the pentagon? Of course we can. So we

can just simply add the five sides together. So we see a is 7 and ea this

together. So we see a is 7 and ea this will be seven. Uh e d will be seven as well. So it's 7 + 7 + 3 8 + b which will

well. So it's 7 + 7 + 3 8 + b which will be four and plus ab which is 10. So we

add the five sides together this will be 31 cm. So after we are done with the

31 cm. So after we are done with the question it lies do a quick summary here. Now in this question they give us

here. Now in this question they give us this irregular shape where we cannot find the perimeter directly.

But one thing we can notice is that this question have given us one special angle error. What is it? Huh? So is the

error. What is it? Huh? So is the interior angle which is 120° which means the exterior angle will be 60°.

So whenever we see that if the exterior angle this part is 60° what can we do?

Uh we can extend the line to construct the equilateral triangle and by making use of the equal sides of the equilateral triangle we can just simply

solve the question itself. So now

knowing this I have also prepared a practice question for you. So this is making use of same concept. After you

are done with the question and you can post your answer in the comment section or you can contact me directly. We can

discuss the solutions together. Now if

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