a² = 24²+7²
a = 25 units.
b = 7+25
b = 32 units.
c² = 24²+32²
c = 40 units.
d = ½(c)
d = 20 units.
d is the radius of the quarter circle.
Therefore, the required length, ? is;
L...
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the ascribed regular pentagon.
b = ½(180-108)
b = 36°
cos36 = (0.5*8)/c
c = 4.94427191 units.
d² = 2*4.94427191²-2*4.94427191²...
Let the radius of the congruent circles be 1 unit.
Therefore;
Area blue is;
3(area sector with radius 1 unit and angle 60°) - 2(area equilateral triangle with radius 1 unit)
= 3(60π/360...
Calculating r, radius of the circle.
r is;
(17/2)²+(r-5)²=r²
(289/4)+r²-10r+25=r²
(289/4)+25=10r
(389/4)=10r
r = (389/40) mm.
r = 9.725 mm.
Let the side length of the square be 2 units.
tana = 2/1
c = atan(2)°
d = 2a
d = 2atan(2)°
Calculating a.
a² = 1²+1²-2*1*1cos(2atan(2))
a = 1.788854382 units.
e = d-45
e = ((2ata...
Calculating length OB.
a² = 6²+2²
a = √(40)
a = 2√(10) units.
a is AC.
tanb = 6/2
b = atan(3)°
√(40)² = 2√(50)²-2√(50)²cosc
40 = 100-100cosc
cosc = 6/10
c = acos(3/5)°
c is angle A...
Silver area is;
2(area rectangle with length 6 cm and width 3 cm - area quarter circle with radius 3 cm - area sector with radius 6 cm and angle 30° + area sector with radius 6 cm and angle 60°...
Sir Mike Ambrose is the author of the question.
Let the length of the two congruent rectangles be x.
Let their width be y.
Therefore area rectangle is;
x * y
= xy square units.
Area bl...
Let the length of the two congruent rectangle be 1 unit.
Let the width be x.
Therefore;
1 ~ (1+x)
x ~ 1
Cross Multiply.
1/x = (x+1)/1
x²+x-1 = 0
(x+½)²=1+¼
x = -½±½√(5)
Theref...
Let the radius of the inscribed circle be r.
Therefore the radius of the ascribed circle, R will be;
R = √(4²+r²)
R = √(16+r²) units.
Therefore;
Area yellow is;
Area circle with rad...
