Calculating the perimeter of the rectangle (QRSP).
Let MR = NS = a
b = (2+a)
b is the width of the rectangle (RS).
Let PS = QR = c, the length of the rectangle.
It implies;
½*ac = A...
Please, move the above question left/right one time to review the solution.
Thank you.
Radius, r of the inscribed yellow circle is;
4.192325 cm
Sir Mike Ambrose is the author of the question.
Area yellow is;
½(0.63245553204*0.75)sin(atan⅓)
= 0.075 square units.
Area ABC is;
½(3*3.75)sin(2tan⅓)
= 3.375 square units.
Area yell...
Calculating green inscribed triangle area.
Notice.
CM = DM
a = 10-6
a = 4 m²
Therefore, green inscribed triangle area is;
(6+6)-a
= 12-4
= 8 m²
Calculating angle x
Let AC = CD = a.
b² = a²+10²
b = √(a²+100) units.
It implies, observing similar plane shape (right-angled) side length ratios to get a.
a - √(a²+100)
5 - 10
Cr...
½(ab) = 6
ab = 12
b = (12/a) units.
c² = a²+b²
c² = a²+(12/a)²
c² = a²+(144/a²)
c = √(a²+(144/a²)) units.
d = 2+b
d = (2+(12/a)) units.
Calculating a.
It implies;
d = c
(2+(12...
8² = 2a²
a² = 32
a = √(32)
a = 4√(2) units.
a is the side length of the square.
c = a+b
c = (4√(2)+b)
c is the diameter of the circle.
d = ½(c)
d = ½(4√(2)+b) units.
d is the radius o...
Calculating a, radius of the small circle.
b = c
2a = 3+2c
2a-2c = 3
2c = 2a-3
c = ½(2a-3) --- (1).
d = a-½(c)
d = ½(2a-c) units.
It implies;
a² = 1.5²+(½(2a-c))²
a² = (9/4)+¼(...
13² = 16²+11²-2*16*11cosa
169 = 256+121-352cosa
352cosa = 377-169
a = acos(208/352)
a = 53.7784533802°
9² = 16²+17²-2*16*17cosb
81 = 256+289-544cosb
544cosb = 545-81
cosb = 464/544
b = 3...
tana = 10/6
a = atan(5/3)°
b = 180-45-a
b = (135-atan(5/3))°
Or
b = (45+atan(3/5))°
It implies;
(6/sin(135-atan(5/3))) = (c/sin(atan(5/3)))
c = 5.3033008589 units.
Therefore, area...
