xy = 40 ------ (1).
b = 4+x-5
b = x-1
y(x-1) = 20 ------ (2).
At (1)
x = 40/y ------ (3).
Notice;
y is the length or base of the rectangle.
Substituting (3) in (2) to get y.
y((40/y)-1) = 2...
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Making a circle to ascribe A, B, C and E quadrilateral with the circumference of the circle cutting across A, B, C and E.
Therefore;
Angle ABC will be;
½(240) = 120°
Parallelogram ABCD height is;...
Let the inscribed square side be a.
tan60 = a/b
a = √(3)b cm.
Where b is BS = CR
It implies;
b+√(3)b+b = 10
(2+√(3))b = 10
b = 10(2-√(3)) cm.
Therefore;
a = √(3)*10(2-√(3))
a = 10(2√(3)-3) cm....
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½(360-60-60-64-36)
= ½(140)
= 70°
Therefore;
Required angle is;
180-64-70
= 180-134
= 46°
Let the base of the quadrilateral be 1 unit.
(1/sin80) = (a/sin60)
a = 0.87938524157 units.
(0.87938524157/sin80) = (b/sin30)
b = 0.44647558819 units.
c² = 0.44647558819²+1-2*0.44647558819cos110 ...
AD = √(12²+6²)
AD = 6√(5) cm.
Angle AMD = atan(2√(5))°
Angle EBM = (90-ata(2√(5)))°
sin(90-ata(2√(5))) = EM/9
EM = 1.96396101212 cm.
Angle CME = 180-atan(2√(5)) = 102.60438264838°
(CE)² = 9+1.9...
Let a be the side of the inscribed square.
Calculating a.
tan60 = a/b
b = a/(tan60) cm.
Where b is BS = CR.
Therefore;
2b+a = 10
2a/(tan60)+a = 10
a((2/tan60)+1) = 10
a = 10(2√(3)-3) cm.
a = 4.6...
