Can You Solve Grade 9 Homework Question From Japan
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½ b.h = 75 = ½ (y+6).x
(y+6).x = 150
(y+6) /x = y/6
x = 6 (y+6)/y
6(y+6)² = 150.y
6 (y² + 12y +36) = 150y
6y² + 72y + 216 = 150y
6y² - 78y + 216 = 0
y² - 13y + 36 = 0
y = 9 cm ; x = 10 cm
x+y = 19 cm ( Solved √ )
Area(ABC) = Area(BPC)+ Area(APC)
75=½(Y+6)*6 + ½X*6
Y+6+X=25
X+Y=19
*Thales' theorem* is a fundamental theorem of Euclidean geometry as important as *Pytahgore's theorem*
Why don't you use it instead of always going through the similarities of triangles.
I want to remind you that the cases of similarities use Thales' theorem
Directly using Thales' theorem : BQ / BC = BP/ BA = PQ / X ....
Area (ABC) = Area (BPQ) + Area(PQCA)
75 = 6*y/2 +(6+x)*6/2 =3*(x + y) + 18 => x+y = 19
The area of the triangle is 75, so x(y+6)=150. According to Thales’s theorem, (y)/(y+6)=6/x, which results in 6(x+y)=114, so x+y=19.
The answer is x + y = 19. At the 3.40 mark, I now realize that I have been thinking HL similarity a little imprecisely. I should have thought of HL similarity as simply the pair of common sides being set equal to the pair of sides subtended by the 90° angle. I hope that this is an improvement. Please let me know when you can.
from Morocco thank you for your interesting videos and for your clear and complete explanations
Area of triangle PBQ is half of 6×y=3y. Let, PM a perpendicular on AC. So, PM=6 and area of PQCM=6×6=36. Since PM is perpendicular on AC, AM=x-6. Hence, area of PAM= half of 6×(x-6)=3x-18.
So, area of PBQ+PQCM+PAM=75
3y+36+3x-18=75
3x+3y=57
3(x+y)=57
x+y=57/3
x+y=19
What do you guys think?
サムネを見て解けない問題を出してはいけない。三角形ABCの面積が75であることをサムネにも必要だ。
(6)^2 (6^2= {36+36}=72 180°ABCPQY/72x=2.36 2.6^6 2.3^2^3^2 1.1^13^2 3^2(ABCPQYX ➖ 3ABCPQYX+2).
1/2*6*y +36+1/2*6*(x-6)
= 3y+36+3x-18
=3x+3y+18
= 1/2*(y+6)*x
xy +6x =6x+6y+36
xy = 6y +36
xy = 6 *(y+6)
(6+Y)X/2=75 6X+XY=150
6/Y=X/(6+Y) 36+6Y=XY 6X+36+6Y=150 6(X+Y)=114 X+Y=19
(6Y)/2+[(6+X)6]/2=75
6(X+Y)=114
X+Y=19 u.
Very cool!!👍
y is 19
X+Y=19
φ = 30° → sin(3φ) = 1; ∆ ABC→ AB = AP + BP; AC = AD + CD = AD + 6 = x; BC = AQ + CQ = y + 6
sin(BQP) = sin(PDA) = sin(BCA) = 1; APD = PBQ = ABC = δ; x(y + 6) = 150 → x + y = ?
tan(δ) = 6/y = (x - 6)/6 → x = 6(y + 6)/y; x(y + 6) = 150 → x = 150/(y + 6) = 6(y + 6)/y →
y1 = 9; y2 = 4 → y > 6 → y = 9 → 4 = x - 6 → x = 10 → x + y = 19
Easy