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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3695234

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Calculating ratio area yellow square to area red square.Let the side length of the inscribed yellow square be 2 units.It implies yellow square area is;2²= 4 square units.a = (2+x) units.Where x is the side length of the red inscribed square and a is the side length of the ascribed square.b = (2-x) units.Calculating x.(2+x) ~ xx ~ (2-x)Cross Multiply.x² = 4-x²2x² = 4x² = 2x = √(2) units.It implies, area red inscribed square is;x²= √(2)²= 2 square units.Therefore, ratio area yellow square to area...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3693960

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Calculating area A (Area of one of the two inscribed equal squares).Let their side length be x each.a = 4+9a = 13 units.b = x+xb = 2x units.c²+4² = (2x)²c = √(4x²-16) units.d = 2cd = 2√(4x²-16) units.It implies;e ~ x4 ~ 2xCross Multiply.2ex = 4xe = 2 units.f = ½(c)f = ½√(4x²-16) units.g = c-2g = (√(4x²-16)-2) units.tanh = 13/(2√(4x²-16)) --- (1).tanh = (½√(4x²-16))/(√(4x²-16)-2)tanh = = √(4x²-16)/(2√(4x²-16)-4) --- (2).Equating (1) and (2).13/(2√(4x²-16)) = √(4x²-16)/(2√(4x²-16)-4)2(4x²-16) = 2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3693938

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Calculating Area Triangle CBA.Let the two equal lengths of the ascribed isosceles right-angled triangle be x.It implies;4² = 2²+x²-2*2xcosa16 = 4+x²-4xcosa12 = x²-4xcosa --- (1).b = (90-a)°(2√(2))² = 2²+x²-2*2xcosb8 = 4+x²-4xcos(90-a)4 = x²-4x(cos90scosa+sin90sina)4 = x²-4xsina4xsina = x²-4sina = (x²-4)/(4x) --- (2).Calculating cosa from (2).(x²-4) = Opposite.4x = Hypotenuse.Calculating Adjacent, let it be c.c²+(x²-4)² = (4x)²c² = 16x²-x⁴+8x²-16c = √(-x⁴+24x²-16) units.cosa = √(-x⁴+24x²-16)/(4x...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3692550

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Calculating Area Green.a = 12+8a = 20 units.a is BG.tanb = 12/20b = atan(3/5)°b is angle DAH.c = 180-45-bc = (135-atan(3/5))°(12/sin(135-atan(3/5))) = (d/sin(atan(3/5)))d = 6.36396103068 units.d is DI.Therefore, green area is;Area triangle with height and base 12 units respectively - Area triangle with height 6.36396103068sin45 and base 12 units.½*12*12 - ½*6.36396103068sin(45)*12= 72-27= 45 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3692540

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Calculating yellow shaded area (equilateral triangle).Let x be CE.a = 4-3a = 1 unit.b²+3² = x²b = √(x²-9) units.b is AE.c²+4² = x²c = √(x²-16) units.c is BE.d = b+cd = (√(x²-9)+√(x²-16)) units.d is AB.e²+1² = x²e = √(x²-1) units.e is equal d.(√(x²-9)+√(x²-16)) = √(x²-1)(√(x²-9)+√(x²-16))² = x²-1x²-9+2√((x²-9)(x²-16))+x²-16 = x²-12√((x²-9)(x²-16)) = 24-x²4((x²-9)(x²-16)) = (24-x²)²4(x⁴-25x²+144) = 576-48x²+x⁴4x⁴-100x²+576 = 576-48x²+x⁴4x⁴-100x² = -48x²+x⁴3x⁴ = 52x²x² = 52/3 square units.x² is th...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3691854

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Calculating yellow area.Let x be each of the three congruent red lengths.Let y be each of the two congruent blue lengths.a = (x+3) units.It implies;√(129)² = (x+3)²+x²+2x(x+3)cosb129 = 2x²+6x+9+(2x²+6x)cosbcosb = (120-6x-2x²)/(2x²+6x) --- (1).Again.y² = x²+3²+2*3*xcosby² = x²+9+6xcosb --- (2).Again.y² = (x+3)²+x²-2*x(x+3)cosby² = 2x²+6x+9-(2x²+6x)cosb --- (3).Equating (2) and (3).x²+9+6xcosb = 2x²+6x+9-(2x²+6x)cosb6xcosb = x²+6x-(2x²+6x)cosb6xcosb+(2x²+6x)cosb = x²+6x(2x²+12x)cosb = x²+6x2(x²+6...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3691330

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Calculating Area Blue.Let x be the base of the inscribed white right-angled triangle with hypotenuse 10 units.a² = 10²+10²a = √(2(10²))a = 10√(2) units.a is the hypotenuse of the ascribed right-angled triangle.b+90+135 = 360b = 360-90-135b = 270-135b = 135°Notice.The two inscribed blue scalene triangles are similar (they both have equal positions interior angles).It implies;10 ~ 10√(2)x ~ cCross Multiply.10c = 10√(2)xc = √(2)x units.Again.10 ~ 10√(2)√(2)x ~ dCross Multiply.10d = 20xd = 2x units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3691312

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Calculating Area Red.a = ½(10)a = 5 m.a is the radius of each of the two equal green inscribed circles.It implies, area red is;Area triangle with height 20 m and base 10 m - Area circle with radius 5 m.½(20*10) - π(5*5)= 100-25π= 25(4-π) m²= 21.4601836603 m²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3690219

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Calculating Area Blue.a = 6+4a = 10 units.a is OQ.b = a+4b = 10+4b = 14 units.tanc = 6/10c = atan(3/5)°c is angle OQP.tand = 6/14d = atan(3/7)°e = 180-ce = 180-atan(3/5)e = (90+atan(5/3))°e = 149.036243468°f = 180-e-df = 180-149.036243468-atan(3/7)f = 7.76516601835°g = 180-2dg = 180-2atan(3/7)g = 133.602818973°h = e-gh = 149.036243468-133.602818973h = 15.433424495°tanj = 14/6j = atan(7/3)°k = 180-2jk = 180-2atan(7/3)k = 46.3971810273°tanl = 10/6l = atan(5/3)°m = 180-2lm = 180-2atan(5/3)m = 61.9...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3689034

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Calculating Red Area.Notice.45 cm is the side length of the square.a = 45-9-18a = 18 cm.tanb = 45/18b = atan(5/2)°c = 180-bc = 180-atan(5/2)c = (90+atan(2/5))°c = 111.801409486°d = ½(90)d = 45°e = 180-c-de = 180-111.801409486-45e = 23.198590514°It implies;(18/sin23.198590514) = (f/sin111.801409486)f = 42.4264068707 cm.g² = 2(45)²g = 45√(2) cm.g = 63.6396103068 cm.g is the diagonal of the square.h = g-eh = 63.6396103068-42.4264068707h = 21.2132034361 cm.It implies the red area is;2(½*18*42.42640...
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