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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2677371

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Let a be the side length of the square. b = (a-3) m. c = (a-5) m. It implies; 10² = (a-3)²+(a-5)² 100 = a²-6a+9+a²-10a+25 2a²-16a+34-100 = 0 2a²-16a-66 = 0 a²-8a-33 = 0 a²-11a+3a-33 = 0 a(a-11)+3(a-11) = 0 (a-11)(a+3) = 0 It implies; a = 11 m. Area square is; a² = 11² = 121 m²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2671866

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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 Cross Multiply. 10a = 5√(a²+100) 2a = √(a²+100) 4a² = a²+100 3a² = 100 a = √(100/3) a = 10/√(3) a = ⅓(10√(3)) units. The required angle, x is; tanx = a/10 tanx = ⅓(10√(3))/(10) tanx = ⅓√(3) x = atan(⅓√(3)) x = 30°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2668416

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Calculating r, radius of the circle. a = 6+4 a = 10 units. a is AD = AC. b²+6² = 10² b = √(100-36) b = √(64) b = 8 units. c = b-r c = (8-r) units. Therefore, r, radius of the circle is; r² = (8-r)²+4² r² = 64-16r+r²+16 16r = 80 r = 5 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2650290

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Calculating x, angle ABD a = ½(180-x)° a is angle BAD. It implies; x, angle ABD is, x+x+(a+39) = 180 (sum of the interior angles of the ascribed triangle) 2x+½(180-x) = 180-39 2x+½(180-x) = 141 4x+180-x = 282 3x = 282-180 3x = 102 x = 34°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2645027

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Calculating R, radius of the quarter circle. ¼πR²=64π² R = 16√(π) cm Calculating x, radius of the green inscribed semi circle. (2x)²+x²=(16√(π))² Therefore; 5x² = 256π x = (16√(5π))/5 cm It implies; Area green inscribed semi circle is; ½π((16√(5π))/5)² = (256π²)/10 cm² Calculating y, radius of the blue inscribed semi circle. (2y)²+(y+x)²=(16√(π))² Therefore; 4y²+y²+(32√(5π)y)/5+(256π)/5=256π 25y²+32√(5π)y-1024π= 0 y = √(25856π/625)- √(256*5π/625) y = 8.863752...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2638503

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Sir Mike Ambrose is the author of the question. Notice; Side length of the congruent regular hexagon is 2 units. (a) Calculating Length Blue ÷ Length Red. Length Blue is; Let it be x. 4²=2²+x²-4xcos150 x²+2√(3)x-12= 0 It implies; x (Length Blue) = (√(15)-√(3)) units. Length Red is; Let it be y. y = √(8-8cos120)-x y = 2√(3)-(√(15)-√(3)) It implies; y (Length Red) = (3√(3)-√(15)) units. Therefore; Length Blue ÷ Length Red exactly is; (√(15)-√(3)) ÷...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2632458

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a = (10+x) units. a is the radius of the ascribed semi circle. sinb = 16/20 b = asin(4/5)° Calculating x. It implies; (10+x)² = 10²+21²-2*10*21cos(asin(4/5)) (10+x)² = 289 10+x = √(289) 10+x = 17 x = 17-10 x = 7 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2625427

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Let a be the side length of the square. a² = 98 a = √(98) a = 7√(2) cm. tanb = (0.5*7√(2))/(7√(2)) b = atan(1/2)° c = 90-b c = atan(2)° d = 45-b d = (45-atan(1/2))° e = 180-(45-atan(1/2))-atan(2) e = 98.1301023542° f = 135-e f = 36.8698976458° (7√(2)/sin98.1301023542) = (g/sin45) g = 7.0710678119 cm. Therefore, area shaded is; 0.5*7.0710678119*7√(2)sin36.8698976458 = 21 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2625009

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Sir Mike Ambrose is the author of the question. Area Green is; Area triangle two lengths 16/3 units and ⅓√(181) units, and angle 138.0127875°, the angle they form + Area triangle two lengths 8 units and ⅓√(85) units, and angle 102.528807708°, the angle they form. = ½(16/3)(√(181)/3)sin(138.0127875) + ½(8)(√(85)/3)sin(102.528807708)  = 8 + 12 = 20 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2614148

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a = ½(7+13) a = 10 units. a is the radius of the ascribed semi circle. b = 10-7 b = 3 units. Calculating y. 10² = c²+6² c² = 64 c = 8 units. y = b+c y = 11 units. Calculating x. x = 2c-y x = 2*8-11 x = 16-11 x = 5 units. It implies; x = 5 units. y = 11 units.
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