Two Methods to calculate the side length X | (Step-by-step explanation) | #math #maths

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Two Methods to calculate the side length X | (Step-by-step explanation) | #math #maths

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[TurquoizeGoldscraper]

Of course I thought of the second answer, but your first answer was very clever.

[nineko]

I'd personally do:
x² + (100 - x)² = 5018
2x² - 200x + 4982 = 0
x = 53, x = 47, and of course we pick the geometrically correct one.

[HappyFamilyOnline]

Amazing explanation 👍
Thanks for sharing 😊

[MrPaulc]

The first method caught me out. I went straight for the second by x^2 + y^2 = 5018 and x + y = 100. I produced a quadratic via substitution and solved for 53 and 47 with the quadratic formula. It looked a bit unwieldy at
(200+or-sqrt(40, 000 - 4*2*4, 982))/4, but looked easier once realising that the discriminant was 144.

[Copernicusfreud]

Yay! I solved the problem. I used method #2 in the video and the quadratic formula to solve for x.

[Alishbafamilyvlogs-bmip]

So excellent video so amazing keep it up❤❤

[j.r.]

These two methods are arguably just variants of the same method. One is sort of a visual representation of the other. The "obvious" method that you skipped is substitution: y = 100 - x. Plug this into the area equation to get a quadratic in x that can be easily factored and solved.

[himo]

(100-x)^2+x^2=5018
10000-200x+x^2+x^2=5018
2x^2-200x+4982=0
x^2-100x+2491=0 (x-47)(x-53)=0
x>100-x>0, x=53

[arthurschwieger]

At 8:54 you stated that x>Y. As you usually do at the beginning of your videos, you stated that the diagram is not 100% true to the scale. That would indicate that the either the left or the right square is the largest and there are two answers to this problem. X=53 or X=47.

[jarikosonen]

This looks like very good trick to get the x-y from manipulation of (a-b)^2 and (a+b)^2... !

[JamesDavy]

What you have just defined with the big square is the square metre.

[rabbitsproductions]

My method was a blend of the 2 shown. Did the first method until we got the area of the overlapping boxes equal to 36 and figured each side to be 6. Then from that point, since the small overlapping box has a side length of 6 that means the bigger box length minus the smaller box side length would be x-y=6 and from there I used the last few steps of the second method shown

[alster]

3rd method is similar to 2nd method only via substitution

y= 100-x

And plug this to the equation x²+y²= 5018

and we get

2x²-200x+10000= 5018
x²-100x+5000= 2509
x²-100x+2491= 0


Then of course factoring
(This took me time though)

(x-53)(x-47)

x= 53, 47.

Based on the figure, the larger value is more acceptable so x= 53

[devondevon]

x = 53
let side of large square = x, then
side of smaller square = 100- x

x^2 + (100-x)^2 = 5018

x^2 + x^2 -200x + 10, 000 = 5018

2x^2 - 200 x + 4982 =0
x^2 - 100 x + 2491 =0 divide both sides by 2
(x-53)(x-47)=0
x=53 and x=47

the larger of the two = 53 cm,
the other is 47 cm

[kelvinmakungu]

Thinking about it, both methods are the same, one is just more visual while the second is more mathematically oriented

[fsyi]

The first method is better with no doubts

[ErnstNL]

Are there any rules for adding or subtracting equations? This approach is applied from time to time, but I always seem to miss that opportunity. Thanks.

[mohanbhaipatel]

How combined area can be more than the Big Square ?.

[kennethstevenson]

I used side length (100 - x ) for the smaller square which produced the equation (100 - x )^2 + x^2 = 5018 which when simplified produced X = 53 cm.

[christopherellis]

The first method counted the area of the overlap twice
x=50+18^½ = 54 24...