Sir Mike Ambrose is the author of the question.
Let the width of the rectangle be x and the length be y.
Let the unknown inscribed length of the rectangle be z.
Calculating z.
√(74)²+√(58)...
r = 5√(145)/8 unit.
Please, move the above question one time, right/left to review the solution.
Thank you.
Let a be the radius of the circle.
b = (a-1) units.
7² = a²+b²-2abcosc --- (1).
11² = a²+b²+2abcosc --- (2).
At (1).
7² = a²+b²-2abcosc
2abcosc = a²+b²-49 --- (3).
Substituting (...
Calculating length x.
a = 4+3
a = 7 units.
a is the side length of a ascribed square.
b² = 2*7²
b = 7√(2) units.
b is the diagonal of the ascribed square.
Let the side length of the in...
Yellow area is;
Area semi circle with radius 12 units - Area semi circle with radius 9 units - Area semi circle with radius 3 units.
= ½(12²π) - ½(9²π) - ½(3²π)
= ½(144π-81π-9π)
= ½(54π)
=...
Area of the isosceles triangle is;
The radius of the semi circle is 10 units.
Therefore the single side length of the square is;
2 * 10 = 20 units.
Therefore red area is;
Area triang...
Let the side length of the congruent square be 1 unit.
Therefore area of the shape is;
8 square unit.
Shaded area is;
Area triangle with two length √(2) units and √(5)/4 units, and angl...
Yellow area is;
12(area equilateral triangle with radius 2 units)
= 12(½(4)sin60)
= 24sin60
= 12√(3) square units.
Let k = 1 unit.
a = 5+1
a= 6 units.
a is the side length of the square.
b = ½(a)
b = 3 units.
c = b-1
c = 2 units.
tand = 6/2
d = atan(3)°
e = (180-atan(3))°
It implies;
(...
Let the radius of the ascribed circle be 1 unit.
Therefore;
Area blue is;
12(area sector with radius 1 unit and angle 60° - area equilateral triangle with single side length 1 unit).
=...
