Calculating Length x.
7² = x²+(x+5)²-2*(5+x)xcosa
49 = 2x²+10x+25-(10x+2x²)cosa
(10x+2x²)cosa = 2x²+10x-24
cosa = (2x²+10x-24)/(10x+2x²) --- (1).
7² = x²+5²+2*x*5cosa
49-25-x² = 10xcosa
24-x² = 10...
Calculating length c.
cosd = 9/12
d = acos(3/4)°
e = 2d
e = 2acos(¾)°
Therefore, length c is;
cose = c/a
cos(2acos(¾)) = c/12
c = 12cos(2acos(¾))
c = 12*⅛
c = ½(3) units.
c = 1.5 units.
Let a be the diameter of the circle.
x² = 6²+6²+2*6*6cosb
x² = 72+72cosb --- (1).
x² = 14²+a²-2*14acosb
x² = 196+a²-28acosb --- (2).
Notice.
x is length AC
b is angle ADC.
cosb =...
Let a = AB = AD = CD.
b² = 2a²
b = √(2)a units.
b is BD.
Notice.
Triangle BCD is a right-angled triangle, where BC is the hypotenuse.
c² =(√(2)a)²+a²
c = 3a²
c = √(3)a units.
c is BC.
cosd = (0....
Sir Mike Ambrose is the author of the question.
Calculating Exactly Green Area.
Let x be the side length of each of the three inscribed congruent squares.
a² = 2x²
a = √(2)x
a is the diago...
Let a be the radius of the quarter circle.
b = (a-6) units.
c = (a-8) units.
Let x be the side length of the square.
x² = (a-8)²+(a-6)²
x² = a²-16a+64+a²-12a+36
x² = 2a²-28a+100
x =...
Calculating the radius of the inscribed circle.
a²+6² = 10²
a = √(64)
a = 8 units.
Let x be the radius of the inscribed half circle.
Calculating x.
b = (8-x) units.
c = (6-x) units.
It implies...
Let the three equal lengths be x.
a = x+x+x+8+8
a = (16+3x) units.
a is the diameter of the ascribed half circle.
b = ½(a)
b = ½(16+3x) units.
b is the radius of the ascribed half circle....
Calculating r2, radius of the smaller inscribed circle.
r2 will be;
Let it be x.
Therefore;
(4+x)²=(8-x)²+(4-x)²
16+8x+x²=64-16x+x²+16-8x+x²
x²-32x+64=0
(x-16)²=-64+256
x = 16±8√(3)
x ≠ 16...
Kindly move the question left/right one time to review the analysis of the question (plane shape).
Thank you nicely.
Calculating R, radius of the quarter circle.
a = 3+4
a = 7 units.
b² = 2...
