Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3629775

Calculating r, radius of the inscribed circle.Notice.125π cm² is the total area of the five congruent green circles.Calculating their radius, let it be x.5*πx² = 125πx² = 25x = √(25)x = 5 cm.Again, x is the radius of each of the five congruent circles.Notice.The radius of the five congruent green circles will connect to form a regular pentagon with side 10 cm.a = ⅕*180(5-2)a = ⅕*180*3a = 108°a is the single interior angle of the derived regular pentagon with side 10 cm.b = ½(a)b = ½(108)b = 54°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3629772

Calculating length h.Let x be the radius of the half circle.x² = 4²+3²x = √(25)x = 5 cm.Again, x is the radius of the half circle.4² = y²+a²a² = 16-y²a = √(16-y²) cm.a is half length h.b = (5-y) cm.Calculating y.a²+b² = 5²√(16-y²)²+(5-y)² = 5²16-y²+25-10y+y² = 2516 = 10yy = ⅕(8) cmy = 1.6 cm.Recall.a = √(16-y²)And y = 1.6 cm.a = √(16-1.6²)a = ⅕(4√(21)) cm.a = 3.66606055596 cm.It implies, length h is;h = 2ah = 2*⅕(4√(21))h = ⅕(8√(21)) cm.h = 7.33212111193 cm.OrCalculating length h.cosc = y/4c =...

Mathematics Question and Solution

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Calculating Area Blue.Let x be the side length of the inscribed regular pentagon.a = ⅕*180(5-2)a = 108°a is the single interior angle of the inscribed regular pentagon.b² = 2x²-2x²cos108b = 1.61803398875x units.c²+(0.5x))² = (1.61803398875x)²c² = 2.61803398875x²-0.25x²c = √(2.36803398875x²)c = 1.53884176859x units.c is the height of the inscribed regular pentagon and also the height of the ascribed isosceles trapezoid.d = 120-90d = 30°cos30 = e/4e = 4cos30e = 2√(3) units.e = 3.46410161514 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3628855

Calculating Area Green.Notice.The composite plane shape is drawn to scale.a = 6 cm.Let b = x cm.b is the width of the inscribed rectangle.c = 2x cm.c is the length of the inscribed rectangle.d² = x²+(½(x))²d² = x²+¼(x)²d = √(¼(5x²))d = ½√(5)x cm.d is the radius of the circle.e = 2de = 2*½√(5)xe = √(5)x cm.e is the diameter of the circle.Calculating x.2x ~ 6√(5)x ~ ½√(5)xCross Multiply.√(5)x² = 6√(5)x√(5)x = 6√(5)x = 6 cm.Again, x is the width of the inscribed rectangle.Recall.c = 2xAnd x = 6 cm...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3628853

Calculating Area Green Square.Let x be the side length of the green square.a = (100-x) m.a is the side length of the orange square.Calculating x.x²+(100-x)² = 5018x²+10000-200x+x² = 50182x²-200x+10000-5018 = 0 x²-100x+5000-2509 = 0x²-100x+2491 = 0(x-50)² = -2491+(-50)²(x-50)² = 9x-50 = ±√(9)x = 50±3Therefore;x ≠ 50+3 ≠ 53 m.x = 50-3 = 47 m.Again, x is the side length of the green square.It implies, area green square is;x²= 47²= 2209 m²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3628851

Calculating pink area.Notice.The triangle is equilateral.a = 90-60a = 30°tan30 = b/2b = ⅓(2√(3)) m.It implies;Area pink is;Area square with side 2 m - Area triangle with height 2 m and base ⅓(2√(3)) m.2²-½(2*⅓(2√(3)))= 4-⅓(2√(3))= ⅓(12-2√(3)) m²= 2.84529946162 m²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3628850

Calculating x, length OP.a² = 2²+6²a = √(40) units.a is BC.tanb = 6/2b = atan(3)°b is angle PBC.cosc = (0.5√(40))/√(50)c = acos(√(10)/√(50))c is angle PBC.d = b-cd = atan(3)-acos(√(10)/√(50))d = 8.13010235416°d is angle PBO.It implies, length x is;x² = 2²+√(50)²-2*2√(50)cos8.13010235416x² = 54-4√(50)cos8.13010235416x = √(26) units.x = 5.09901951359 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3628849

Calculating Area Green Circle.Let x be the radius of the circle.x is the height of the pink area.a = x+⅓(x)a = ⅓(4x) cm.a is the base of the pink area.Calculating x².½*x*⅓(4x) = 27⅓(2x²) = 272x² = 81x² = ½(81) cm²Again, x is the radius of the green circle.Area Green Circle is;πx²= ½(81π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3627179

Calculating Area Pink Square.a = √(2) m.a is the side length of the green square.b = √(1)b = 1 m.b is the side length of the purple square.Let x be the side length of the pink square.c²+√(2)² = x²c² = x²-2c = √(x²-2) m.Calculating x².sind = 1/x --- (1).sind = √(x²-2)/x --- (2).Equating (1) and (2).1/x = √(x²-2)/x1 = √(x²-2)1 = x²-2x² = 1+2x² = 3 m²x² is the area of the pink square.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3627173

Calculating R, radius of the circle.a = ½(24)a = 12 units.b²+12² = R²b² = R²-144b = √(R²-144) units.c = 24 units.d = R+bd = (R+√(R²-144)) units.Notice.c = dTherefore R, radius of the circle is;R+√(R²-144) = 24√(R²-144) = 24-RR²-144 = (24-R)²R²-144 = 576-48R+R²48R = 576+14448R = 7204R = 60R = 15 units.

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