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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2761562

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Let the length of the two congruent rectangle be 1 unit. Let the width be x. Therefore; 1 ~ (1+x) x ~ 1 Cross Multiply. 1/x = (x+1)/1 x²+x-1 = 0 (x+½)²=1+¼ x = -½±½√(5) Therefore; x ≠ -½(1+√(5)) units. x = ½(√(5)-1) units. Let alpha be y. Therefore; Tany = (1+x)/1 Tany = (1+x) And x = ½(√(5)-1) unit. Tany = ½(√(5)-1)+1 Tany = ½√(5)-½+1 Tany = ½√(5)+½ Tany = ½(1+√(5)) Therefore; Tany = Tan alpha = Golden Ratio

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2761548

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Let the radius of the inscribed circle be r. Therefore the radius of the ascribed circle, R will be; R = √(4²+r²) R = √(16+r²) units. Therefore; Area yellow is; Area circle with radius √(16+r²) units - Area circle with radius r units. = π(√(16+r²))² - πr² = π(16+r²) - πr² = 16π + πr² - πr² = 16π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2761531

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Let the side length of the large square be 4 units. Therefore; The side length of the blue inscribed square is; 4-(4√(3)/3) = ⅓(12-4√(3)) units. Therefore; Side blue square : Side large square is; ⅓(12-4√(3)) : 4 = (12-4√(3))/12 = ⅓(3-√(3)) = 0.42264973081

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2761266

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The width of the rectangle is; R units. The length of the rectangle is; = √((R+6)²-(R-6)²) = √(R²+12R+36-R²+12R-36) = √(24R) units. Therefore; √(24R) * R = 243 24R³ = 243² R³ = 2460.375 R = (2460.375)^(⅓) R = 13.5 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2760797

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Please, move the above question left/right one time to review the solution. Thank you. Area Shaded/blue or purple is; = 8√(2)sin15 cm² = 2.92820323028 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2760466

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Shaded area is; Area sector with radius 10 units and angle acos(0.7) - Area triangle with height √(51) units and base 7 units - area sector with radius 3 units and angle 81.37307344° - area sector with radius10 units and angle 17.2538531174° + area triangle with two sides length 10 units, and angle 17.2538531174° = (acos(0.7)*1))π÷360) - ½(√(51)*7) - (9π*81.37307344)/360 -(100π*17.2538531174)/360 + ½(100)sin17.2538531174 = 39.7699415092 - 24.9949994999 - 6.39102624298 - 15.0568272777 +...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2760268

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Calculating the area of the inscribed regular pentagon. Let the single side length of the inscribed regular pentagon be x. 12²=2y²-2y²cos108 y = √(144/(2-2cos108)) y = 7.416407865 cm. Therefore; x = √(2(7.416407865)²-2(7.416407865)²cos36) x = 4.58359213501 cm. Therefore area inscribed regular pentagon is; (5*4.58359213501²)/(4tan(36)) = 36.1460548598 cm².

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2760264

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Please, move the above question left/right one time to review the solution. Thank you. AO : OB is; = 5 : 3

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2760251

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Sir Mike Ambrose is the author of the question. Calculating letter k considering yellow area (trapezoid). It implies; Half the sum of two parallel length (54+4k²)/9 units and (54+10k²)/9 units, multiply height 3k units is equal yellow area. And yellow area = 117 square units. Therefore; ½(3k)(108+10k²)/9=117 7k³+54k-351=0 It implies; k = 3 unit. Therefore; Area green is; Area trapezoid with two parallel length 10 units and 6 units, and height 6 units. = ½(16)*6 =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2759908

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Shaded area is;  Area semi circle with radius 7cm + Area rectangle with length 14 cm and width 7 cm - Area semi circle with radius 7cm. = ½(49π) + (14*7) - ½(49π) = 98 cm² Or Shaded Area is; Area rectangle with length 14 cm and width 7 cm. = 14*7 = 98 cm²
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