Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3181185

Calculating Length x. x ~ ½(2) (2+7) ~ x Cross Multiply. x² = 9 x = √(9) x = 3 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3181184

Calculating Area Blue Triangle. a² = 2(2)² a = 2√(2) units. a is the diagonal of a square. b = ½(180-30) b = 75° c = b-45 c = 75-45 c = 30° sin30 = d/a ½ = d/(2√(2)) d = √(2) units. d is the base of the blue triangle. cos30 = e/a ½√(3) = e/(2√(2)) 2e = 2√(6) e = √(6) units. e is the height of the blue triangle. Area Blue Triangle is; ½*de = ½*√(2)*√(6) = ½*2√(3) = √(3) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3179895

Calculating r/R. Let let the ascribed square side length be 2 units. Calculating R. a = ½(2) a = 1 unit. b = (2-R) units. Therefore; (2-R)² = R²+1 4-4R+R² = R²+1 4-1 = 4R R = ¾ units. Calculating r. c²+1² = 2² c = √(3) units. d = (2-r) units. e = (2+r) units. Therefore; (2+r)² = 1²+(2-r)² 4+4r+r² = 1+4-4r+r² 8r = 1 r = ⅛ units. Therefore; r/R is; ⅛ ÷ ¾ = ⅙

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3179893

Calculating Shaded Fraction. Let the ascribed square side length be 5 units. a = 1 unit. a is the side length of the big inscribed yellow square. b = ½(5-a) b = ½(5-1) b = 2 units. b is the side length of the bigger inscribed yellow square. c² = 2²+1² c = √(4+1) c = √(5) units. c is the side length of the biggest inscribed yellow square. Therefore, total shaded yellow area is; 1²+2²+√(5)² = 1+4+5 = 10 square units. It implies, shaded yellow area fraction is; Area shaded ÷ Area of the as...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3178822

Calculating the required angle. Let it be x. a = ⅑*180(9-2) a = 20*7 a = 140° a is the single interior angle of the regular nonagon. b = ½(140)-65 b = 5° c = ½(180(5-2)-3(140)) c = ½(540-420) c = ½(120) c = 60° d = 140-c d = 80° e = ½(140)-c e = 70-60 e = 10° Let the side length of the regular nonagon be 2 units. f² = 2(2)²-2(2)²cos140 f = 3.75877048314 units. g = 70-½(180-140)+5 g = 70-20+5 g = 55° f = 140-20-½(360-2(140)) f = 140-20-40 f = 80° g = 180-55-80 g = 45° (h/sin80) = (3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3178623

Calculating Length x. Let a be the side length of the blue square. b² = 2a² b = √(2)a units. b is the diagonal of the blue square. It implies; x ~ 3 √(2)a ~ a Cross Multiply. ax = 3√(2)a It implies; x = 3√(2) units. x = 4.24264068712 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3178622

Calculating Red Area. Let AB = CD = x. Let AD = BC = y. ½*xa = 10 a = 20/x units. a is BQ. ½*xb = 6 b = 12/x units. b is the horizontal height of area 6 (area triangle APB). c = y-b c = y-(12/x) c = (xy-12)/x units. c is the horizontal height of triangle CPD (red area). d = y-a d = y-(20/x) d = (xy-20)/x units. d is CQ. ½*e*(20/x) = 4 10e = 4x e = ⅖(x) units. e is the vertical height of area 4 (area triangle BPQ). Therefore; Calculating Area Rectangle ABCD (xy). ½*x*(xy-12)/x+½*(xy-2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3177715

Calculating area ABCD. Let x be the radius of the inscribed circle. a = ½(16) a = 8 units. x² = 8²+a² a = √(x²-64) units. b = ½(25) units. It implies; x ~ 8 ½(25) ~ x Cross Multiply. x² = 100 x = 10 units. Again, x is the radius of the inscribed circle. c = 2x c = 20 units. c is the diameter of the inscribed circle, and also, the height of the isosceles trapezoid. sind = 10/(0.5*25) d = asin(20/25) d = asin(4/5)° tan(asin(4/5)) = 20/f f = 15 units. g = x-√(10²-(0.5*16)²) g = 10-√(1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3177285

Calculating Area Yellow. ½*a²sin60 = 24 √(3)a² = 24*4 a² = 96/√(3) a = √(96/√(3)) a = 7.44483887282 units. a is the radius of the circle. b = a-x b = (7.44483887282-x) units. Calculating x. tan60 = (7.44483887282-x)/x √(3)x = (7.44483887282-x) (√(3)+1)x = 7.44483887282 x = 7.44483887282/(√(3)+1) x = 2.72500015453 units. cos30 = x/c c = 2.72500015453/cos30 c = 3.14655914552 units. d = a-c d = 7.44483887282-3.14655914552 d = 4.2982797273 units. It implies, ar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3177282

Sir Mike Ambrose is the author of the question. Let the single side length of the square be 2 units. Area square is; 2² = 4 square units. Calculating green area. It will be; Area square of side 2 units - area triangle of two equal lengths ⅔(√(3)) units and angle 120°, the angle they form - area triangle of lengths (4-2√(3)) units and 2 units, and angle 60°, the angle they form. It implies; 4 - ½(⅔(√(3)))²sin120 - ½*2(4-2√(3))sin60 = 4 - ⅓√(3) - (2√(3)-3) = 4 - ⅓√(3) -2√(3) + 3 = 7 -...

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Mathematics Question and Solution

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