Can you find area of the Green shaded rectangle? | (3 Methods) | #math #maths | #geometry

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Can you find area of the Green shaded rectangle? | (3 Methods) | #math #maths | #geometry

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[AmirgabYT]

205 cm².
Let sides of green rectangle be x and y (width x and length y).
Then:
9y-xy=119
On the other hand:
11y-xy=191
Let's make a system:
9y-xy=119 (1)
11y-xy=191 (2)
Then, let's multiply all the sides of equation (1) by 11, and all the sides of equation (2) by 9. Then we get:
99y-11xy=1309 (1)
99y-9xy=1719 (2)
Let's substracti (2) from (1).

99y-99y-11xy-(-9xy)=1309-1719
-11xy+9xy=-410
-2xy=-410
xy=205
But xy is an area of rectangle, so the answer is 205 cm².
Pin please 🙏

[highlyeducatedtrucker]

Never have the words "This figure may not be 100% true to the scale" been so accurate! 😆

[JamesDavy]

Basically, first method was solving by elimination, second method was solving by comparison and third method was solving by substitution.

[yalchingedikgedik]

That’s very nice and useful solving in many methods .
Thanks Sir for supports
Good luck
❤❤❤❤❤

[michaeldoerr]

The answer is 205 cm squared. I thought that the third method was subtle and much simpler to understand. I am wondering if there is a playlist of geometry problems that showcase THREE methods.

[prossvay]

Let A is.Green rectangle area and x is Width of rectangle
119+A=9x (1)
191+A=11x (2)
(2)-(1)
191-119+A-A=11x-9x
So x=36
(1) 119+A=9(36)
So A=205 cm^2.❤❤❤

[ChuzzleFriends]

Partition the blue rectangle in such a way, it creates two smaller rectangles. A new yellow rectangle with an area of 119 cm², and a new blue rectangle with an area of 72 cm², such that the new yellow one is adjacent to the green rectangle and the new blue one is adjacent to the new yellow one.
So, the distance from the bottom left vertex of the green rectangle to the bottom right vertex of the new yellow one is 9 cm by the Parallelogram Opposite Sides Theorem.
The length of the new blue rectangle is 2 cm.
A = lw
72 = 2w
w = 36
The width of the rectangles is 36 cm.
119 = 36l
l = 119/36
The length of the new yellow rectangle is 119/36 cm.
So, the length of the green rectangle is 11 - 2 - 119/36, or 205/36 cm.
A = (205/36) * 36
= 205
So, the area of the green rectangle is 205 square centimeters.

[Waldlaeufer]

(119 + x) : 9 = (191 + x) : 11
11 (119 + x) = 9 (191 + x)
1309 + 11x = 1719 + 9x
2x = 410
x = 205 cm^2

[SidneiMV]

A = bh

(9 - b)h = 119
(11 - b)h = 191

2h = 72 => h = 36

20h - 2bh = 310
2bh = 720 - 310 = 410

*A = bh = 205*

[sagarmajumder]

Can you make a playlist for the geometry problems?😊

[alster]

Very easy especially the first method.

Solved it on my own and got 205 cm² (I suddenly remembered one of your previous videos).

[marcgriselhubert]

x the length of the green rectangle and h its height (and the height of the yellow and blue rectangles)
We have (9 - x).h = 119 and (11 - x).h = 191. By difference 2.h = 72, so h = 36. So 9 - x = 119/36 and x = 9 - 119/36 = 205/36
Finally the area of the green rectangle is x.h = (205/36).36 = 205. (Very easy)

[Birol]

My way of solution ▶
the wide of the given rectangle: a
this is equal to the one side of the given three smaller rectangles.

the other side of the green rectangle: x
⇒
Ayellow= 119 cm²
119= a*(9-x)

Agreen= ax

Ablue= a(11-x)
191= a(11-x)
⇒
119= a(9-x)
191= a(11-x)
when we divide these two equations into each other we get:
119/191= (9-x)/(11-x)
119*(11-x)=191*(9-x)
1309-119x= 1719-191x
x= 410/72
x= 205/36

119= a(9-x)
a= 119/(9-x)
a= 119/(9- 205/36)
a= 119/(119/36)
a= 36 cm

Agreen= ax
Agreen= 36*(205/36)
Agreen= 205 cm²

[AdityaSharma-rltu]

I calculated this mentally.
Let the area of green rectangle be A and the height be h

119+A=9h
h=(119+A) /9

Similarly
191+A=11h
h=(191+A) /11

Equate both the equations and you will get A=205

[nandisaand]

Method #3
Area Green = b•h
(9-b)•h=119
(11-b)•h=191
119/(9-b)=h=191/(11-b)
119(11-b)=191(9-b)

1309-119b=1719-191b
-1309 +191b -1309 +191b
410=72b
/72 /72
B=5.69
H=(119/(9-5.69))=35.95
Area=5.69•35.95=204.56

[cyruschang]

(9 - x)/(11 - x) = 119/191
191(9 - x) = 119(11 - x)
(191 - 119)x = 191(9) - 119(11)
x = (191(9) - 119(11))/72 = (1719 - 1309)/72 = 410/72 = 205/36
green area = (119x)/(9 - x) cm^2 = (119)( 205/36)/(9 - (205/36)) cm^2 = (119)( 205/36)/(119/36) cm^2 = 205 cm^2

[gavindeane]

Blue is 2cm wider than yellow and has 72cm² greater area, therefore the height must be 72/2 = 36cm.

36 × (9+11) gives the area of blue + area of yellow + (2 × area of green)

720 = 119 + 191 + (2 × green)

So the green area is

(720 - (119+191)) / 2

(720 - 310) / 2

410 / 2

= 205 cm²

[santokhsidhuatla]

11h=191+A
9h=119+A
By subtracting 2) from 1)
2h=72
h=72/2=36
Width for A=
9-119/36=5.69444
A=5.694444x36= 205 cm^2


11-191/36=5.694444
A=5.694444x36=205 cm^2

[santiagoarosam]

(191-119)/(11-9)=36 cm²/cm---> Área verde =(36*9)-119 =205 cm² =(36*11)-191.
Gracias y saludos.

[misterenter-izrz]

The difficulty is rather unevenly, relative to yesterday's puzzle, that is too trivial.😮 (191+A)/(A+119)=11/9, 2A=9×191-11×119=410, A=205.😂