Let the length of the two congruent rectangle be 1 units.
Let the width be x.
Therefore;
1 ~ (1+x)
x ~ 1
It implies;
1/x = (x+1)/1
x²+x-1 = 0
(x+½)²=1+¼
x = -½±½√(5)
Therefore...
Let the side length of the blue inscribed equilateral triangle be 1 unit.
Area blue equilateral triangle is,
0.5*1²*sin60
= ¼√(3) square units.
= 0.4330127019 square units.
It implies;...
Sir Mike Ambrose is the author of the question.
The equation of the curve is;
Using the points;
(4, 4), (2, 0), (12, 0)
And, y =ax²+bx+c
Therefore;
4=16a+4b+c
0=4a+2b+c
0=144a+12b...
Sir Mike Ambrose is the author of the question.
Area BDE is;
Area triangle with side 2 units and 3 units, and angle 120°
= ¼(6√(3))
= ½(3√(3)) square units.
= 2.59807621135 square units....
Sir Mike Ambrose is the author of the question.
Let the single side length of the regular hexagon be 2 units.
Therefore;
Area regular pentagon is;
5(2.12920428618)²÷(4tan(180/5))
= 7.79980...
6²+6²-2*6*6cosa = 12²+3²+2*12*3cosa
72-72cosa = 153+72cosa
144cosa = 81
a = acos(9/16)
a = 55.7711336722°
b = 180-a
b = 124.2288663278°
6²+12²-2*6*12cosc = 6²+3²+2*6*3cosc
180-144cosc =...
tana = 5/11
a = atan(5/11)°
sin(atan(5/11)) = 5/b
b = 12.0830459736 cm.
c = b-2.5
c = 9.5830459736 cm.
sin(atan(5/11)) = d/9.5830459736
d = 3.9654926392 cm.
5/11 = 3.9654926392/e
e...
Let the side length of the ascribed square be 1 unit.
tanc = 0.5/1
c = atan(½)°
cos(atan(½)) = a/1
a = 0.894427191 units.
d² = 2(1²)
d= √(2) units.
d is the diagonal of the ascribed sq...
Let a be the radius of the circle.
b²+2² = a²
b = √(a²-4) units.
c = 5+2
c = 7 units.
d = 3a units.
It implies;
Calculating a.
(3a)² = √(a²-4)²+7²
9a² = a²-4+49
8a² = 45
a =...
tana = 3/4
a = atan(¾)°
a is angle ACB.
Let b be the radius of the three inscribed congruent circles.
c = (4-5b) units.
Calculating b.
tan(0.5atan(¾)) = b/(4-5b)
⅓ = b/(4-5b)
3b = 4...
