Calculate area of the Yellow Square | Blue, Green, and Yellow Squares | Important skills explained

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Calculate area of the Yellow Square | Blue, Green, and Yellow Squares | Important skills explained

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[jaybawaskar]

Best videos best explanation thx for your valuable support

[yalchingedikgedik]

Thanks PreMath
Very well and understandable method

[HappyFamilyOnline]

Very well explained👍
Thanks for sharing🌺🌺

[annatygrys]

The side of the green square =a Than : a^2 - (a - 10)^2 =240 a^2 - a^2 - 100+20a=240 20 a=340 a=17 area of green=G=289 Side of the blue one =17 - 10=7 area B=49 Side of the yellow one y=28-17=11 Area Y=121 Blessings!

[yuusufliibaan]

Good lesson thank you very much dear teacher

[spiderjump]

Let side length of smallest square =a
(a+10)^2 —a^2=20a+100=240

a=7
Side length of largest square =17
Side of yellow sq= 11
Area of yellow square =121

[MrPaulc]

Great video once again. I used different variable names but using yours, I went for 28-c = 10+b which gave me 18-c=b. I set up a second equation with (28-c)^2 - 240 = b^2 which is the equivalent of (28-c)^2 - 240 = (18-c)^2
Ended up with variables of 7 and 11 of which c was 11. I found the third variable unnecessary.

[manojitmaity]

Sir do you engage your whole day in discovering these problems???

[williamwingo]

A slightly different approach:
a^2 -- (a -- 10)^2 = 240; multiply out (a -- 10)^2:
a^2 -- (a^2 -- 20 a + 100) = 240; remove the parentheses by reversing the signs within;
a^2 -- a^2 + 20 a -- 100 = 240; the a^2 term subtracts out and add 100 to both sides:
20 a = 340; divide both sides by 20:
a = 340/20 = 17; a + c = 28, so
c = 28 -- a = 28 -- 17 = 11; and voila!
c^2 = 11^2 = 121.
Cheers. 🤠

[alster]

Easy Geometry problem

There are 2 faster ways to find b at 2:26 is substitution right off the bat

a²-b²= 240

(a+b)(a-b)= 240

Since a= b+10, we substitute this in the above equation

(b+10+b)(b+10-b)= 240

(2b+10)(10)= 240
2b+10= 24
b+5= 12
b= 7 units
a= 17 units
Since a+c= 28
17+c= 28

c= 11

So c²= A(Yellow) = 121 sq units


Or the fastest way is

(b+10)²-b²= 240

b²+20b+100-b²= 240
20b+100= 240
b+5= 12
b = 7
a= 17
c= 11

Still getting the same area of 121 sq units.

[waynevenables]

Forgive me being confused. If the green area minus the blue area equals 240, is the area of the green area 240 ?

[devondevon]

121 Answer
Let the length of blue = x, then area =x^2; hence
length of green = x+10 and area of green = x^2 + 20x+ 100
Since the area of green - the area of blue = 240 (given), then
(x^2 + 20x+ 100)- (x^2)= 240
20x + 100 = 240
20x = 140
x =7 ( the length of blue); hence length of green= 17
Since the length of green + yellow = 28, then yellow's length = 11; hence area of yellow 11^2 or 121

[miguelgnievesl]

I solved it with a single unknown. I started with the yellow square whose side is a; then the side of the green square is 28-a and the side of the blue square is 28-a-10=18-a. Now A(green)=(28-a)² and A(blue)=(18-a)². We have to (28-a)² - (18-a)² = 240. We solve the equation and obtain that a=11. Consequently A(yellow)=121; A(green)=289 and A(blue)=49.

[batavuskoga]

I solved it in another way
A1=area blue circle, side blue square=x
A2=area green circle, side green square=y
A3=area yellow circle, side yellow square=z
A2-A1=240
y=x+10, y+z=28
A1=x²
A2=y²=(x+10)²=x²+20x+100
A2-A1=240 --> x²+20x+100-x²=240 --> 20x=140 --> x=7
y=x+10 --> y=17
y+z=28 --> z=11
A3=area yellow circle=z²=11²=121