Nice to see different methods for solving these problems. Here's a third method: Let A = area of center (yellow) rectangle Combined area of yellow and blue rectangles = A + 80 (with base = 32) Combined area of yellow and green rectangles = A + 176 (with base = 40) Since these rectangles have same height, the ratio of their areas = ratio of their bases: (A + 80) / (A + 176) = 32 / 40 (A + 80) / (A + 176) = 4 / 5 5A + 400 = 4A + 704 5A - 4A = 704 - 400 A = 304
I just mentally calculated that green had 8 cm longer base and 96 cmsq more area so ht is 12. Width of blue is 80/12 and that is 6 2/3, gr base is 14 2/3. Width of yellow is 40-14 2/3 or 25 1/3. 25 1/3 base times 12 ht is 304.
Traditional method of solving equated equations is really defining a past participle. The Woke version of solving we come out of the darkness of the box and wallah!...Boom! ,.... we see the light and readily come up with the answer. 🙂
Blue rectangle Area = 80 = b.H b = 80 / H Green rectangle: Area = 176 = B.H B = 176 / H Total Base of larger rectangle: 40.+ (80/ H) = 32 + (176 / H) 40 - 32 = 176 / H - 80 / H 8 = 96 / H H = 96 / 8 H = 12 cm Bt = 40 + 80/12 = 46,66 cm Total Area : At = Bt H = 46,66 . 12 At = 560 cm² Yellow area: Aw = At - 80 - 176 Aw = 304 cm² ( Solved √ )
Green Area - Blue area = 176 - 80 = 96 cm² has a base of : b= 40 - 32 = 8 cm Its area is A = b.H. , then H = A/b = 92 / 8 H = 12 cm Yellow area: B = 32 - 80/12 (or 40-176/12 ) A = B. H = (32-80/12).12 A = 304 cm² ( Solved √ )
This channel deserves much more attention considering how much work goes into it. Cheers and thank you for sharing friend
Absolutely!😀
Much appreciated!
So nice of you.
Thank you! Cheers! 😀
تمرين جيد جميل .رسم واضح مرتب. شرح واضح مرتب . شكرا جزيلا لكم والله يحفظكم ويحميكم ويرعاكم جميعا . تحياتنا لكم من غزة فلسطين.
Thanks dear🙏
Height of rectangles = y.
Area of yellow rectangle = A.
A + 80 = 32y.
A + 176 = 40y.
Dividing :-
( A + 176 ) / ( A + 80 ) = 40y / 32y = 5 / 4.
Cross multiplying :-
5 ( A + 80 ) = 4 ( A + 176 )
5A + 400 = 4A + 704.
A = 304.
Thank you! Cheers! 😀
Think this soln is most obvious. No x or y Calc. Or if drop out A then calc y directly. Substitute to get A.
Exactly what I did. Cheers.
The second solution is out of this world...Amazing!
Thanks PreMath .
We are enjoying and learning solve Math. Exercise .
Glad to hear that
Love your outside the box method! Super!
Glad you like it!
Easy and refreshing geometry problem
Great!
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Fantastic alternative method at the end.
Glad you liked it
Thank you! Cheers! 😀
I got to xy-40y=80 and xy-32y=176. A quick inspection told me that 8y=96 so y=12. Exceelent channel. The help is appreciated.
So nice of you.
Thank you! Cheers! 😀
Thanks for video.Good luck sir!!!!!!!!
Thank you too
Very nice, sir.
::::::::
Let the area of yellow rect be A
80+A = 32y.......(1)
176+A =40y......(2)
Divide (2) by (1) and get for A.
So nice of you.
Thank you! Cheers! 😀
Most of us came up with 1st Method.. But the 2nd one is mind blowing.
Glad you liked it
Very nice solution!🥂👍❤️
Awesome!
So nice of you.
Thank you! Cheers! 😀
Nice to see different methods for solving these problems. Here's a third method:
Let A = area of center (yellow) rectangle
Combined area of yellow and blue rectangles = A + 80 (with base = 32)
Combined area of yellow and green rectangles = A + 176 (with base = 40)
Since these rectangles have same height, the ratio of their areas = ratio of their bases:
(A + 80) / (A + 176) = 32 / 40
(A + 80) / (A + 176) = 4 / 5
5A + 400 = 4A + 704
5A - 4A = 704 - 400
A = 304
Thanks for sharing!
thankyou so much dear ❤
You are so welcome!
So nice of you, dear
Thank you! Cheers! 😀
Hi Premath I like your explanation second method is awesome I like your channel
So nice of you.
Thank you so much 🙂
(176-80)/(40-32)=12=Altura → [32-(80/12)]x12=304 =Área amarilla
Gracias y saludos.
Thank you
You're welcome
You are wonderful my friend❤
You are the best, dear
So nice of you.
Thank you! Cheers! 😀
great again!
So nice of you.
Thank you! Cheers! 😀
I solved the problem as Method #1 in the video. I missed the second method. I did get the answer.
Great!
Thank you! Cheers! 😀
(32-x)y=80 (40-x)y=176
80/(32-x)=176/(40-x)
3200-80x=5632-176x 96x=2432
x=76/3 y=12
area of Yellow Rectangle :
xy = 76/3＊12 = 304
Thank you! Cheers! 😀
Let H be the height & X be the width of yellow rectangle.
H*(32 - X) = 80 & H*(40 - X) = 176. H = 12.
HX is the yellow area = 32*12 - 80 = 304.
Thank you! Cheers! 😀
I just mentally calculated that green had 8 cm longer base and 96 cmsq more area so ht is 12. Width of blue is 80/12 and that is 6 2/3, gr base is 14 2/3. Width of yellow is 40-14 2/3 or 25 1/3. 25 1/3 base times 12 ht is 304.
بفرض عرض المستطيل الكلي y
32+176/y=40+80/y
176/y_80/y=40_32
96/y=8 y=12
S+176=40×12
S=304
Let A be the area, A+80/A+176=32/40=4/5, so 5A+400=4A+704, then A=304.😃
Thank you! Cheers! 😀
3 methode: 80/12=6 2/3. 176/12=14 2/3. 32*12=384. 384-80=304. 304/12=25 1/3. 25 1/3 + 14 2/3 = 40 so correct.
2nd method is quicker and easy
Traditional method of solving equated equations is really defining a past participle. The Woke version of solving we come out of the darkness of the box and wallah!...Boom! ,.... we see the light and readily come up with the answer. 🙂
Thanks for sharing!
Ar=196
X=24cm
Blue rectangle
Area = 80 = b.H
b = 80 / H
Green rectangle:
Area = 176 = B.H
B = 176 / H
Total Base of larger rectangle:
40.+ (80/ H) = 32 + (176 / H)
40 - 32 = 176 / H - 80 / H
8 = 96 / H
H = 96 / 8
H = 12 cm
Bt = 40 + 80/12 = 46,66 cm
Total Area :
At = Bt H = 46,66 . 12
At = 560 cm²
Yellow area:
Aw = At - 80 - 176
Aw = 304 cm² ( Solved √ )
Green Area - Blue area =
176 - 80 = 96 cm²
has a base of :
b= 40 - 32 = 8 cm
Its area is A = b.H. , then
H = A/b = 92 / 8
H = 12 cm
Yellow area:
B = 32 - 80/12 (or 40-176/12 )
A = B. H = (32-80/12).12
A = 304 cm² ( Solved √ )