Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3589302

Calculating Square Area.Let x be the side length of the square.a = ½(x) units.It implies;b ~ ½(x)½(x) ~ xCross Multiply.bx = ¼(x²)b = ¼(x) units.Therefore;c² = (¼(x))²+(½(x))²c² = (x²/16)+(x²/4)c = √((x²/16)+(x²/4))c = √(5x²/16)c = ¼√(5)x units.c is the base of the inscribed green right-angled triangle.d² = x²+(½(x))²d² = x²+¼(x)²d = √(x²+¼(x)²)d = √(5x²/4)d = ½√(5)x units.d is the height of the inscribed green right-angled triangle.Calculating x², area of the square.½*c*d = 20½*¼√(5)x*½√(5)x =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3588027

Calculating r2.Let it be x.Therefore;(4+x)²=(8-x)²+(4-x)²16+8x+x²=64-16x+x²+16-8x+x² x²-32x+64=0(x-16)²=-64+256x = 16±8√(3)x ≠ 16+8√(3)x = 16-8√(3)Therefore;x = r2 = 8(2-√(3)) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3587017

Calculating Blue Area.The radius, r of the small inscribed circle is; (5+r)²=2(5-r)²25+10r+r²=50-20r+2r²Thereforer²-30r+25=0(r-15)²=-25+225r = 15±√(200)r = 15±10√(2)It implies;r ≠ 15+10√(2)r = 15-10√(2) units.r = 5(3-2√(2)) units.Therefore area blue is;Area square with side length 5 units - Area quarter circle with radius 5 units - Area circle with radius 15-10√(2) units.5²-¼(5²)π-π(15-10√(2))²= 25-¼(25π)-π(425-300√(2))= 25-¼(25π)-425π+300√(2)π= ¼(100-25π-1700π+1200√(2)π)= ¼(100-1725π+1200√(2)π...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3585819

Calculating length c.d = a+bd = 8+9d = 17 units. e = b-ae = 9-8e = 1 unit.It implies;e²+f² = 17²f² = 289-1f = √(288)f = 12√(2) units.cosg = 1/17g = acos(1/17)g = 86.6277133166°h = 180-gh = 180-86.6277133166h = 93.3722866834°j = ½(g)j = ½(86.6277133166)j = 43.3138566583°k = ½(h)k = ½(93.3722866834)k = 46.6861433417°Therefore, length c is;tan43.3138566583 = c/9c = 9tan43.3138566583c = 8.48528137424 units.Or tan46.6861433417 = c/8c = 8tan46.6861433417c = 8.48528137423 units.Or c = ½(f)c = ½(12√(2)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3584695

Calculating r+R.Notice.DEFG is a square.DG = (9+R) units.FG = R+1+5+1+rFG = (7+R+r) units.Calculating r.Equating DG = FG.9+R = 7+R+r9 = 7+rr = 9-7r = 2 units.Calculating R.AG = 1+5+RAG = (6+R) units.AD = 9+5+1AD = 15 units.It implies;15² = (9+R)²+(6+R)²225 = 81+18R+R²+36+12R+R²2R²+30R-108 = 0R²+15R-54 = 0R²+18R-3R-54 =0R(R+18)-3(R+18) = 0(R+18)(R-3) = 0Therefore;R ≠ -18R = 3 units.It implies;r+R= 2+3= 5 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3583681

Calculating Area Blue Circle.Notice.10 units is the side length of the square.a = (10+2x) units.b = ½(a)b = ½(10+2x)b = (5+x) units.b is the radius of the blue circle.c = b-2xc = 5+x-2xc = (5-x) units.d = ½(10)d = 5 units.Calculating x.b² = c²+d²(5+x)² = (5-x)²+5²25+10x+x² = 25-10x+x²+2520x = 25x = 1.25 units.Recall.b = (5+x) And x = 1.25 units.b = 5+1.25b = 6.25 units.Again, b is the radius of the blue circle.Therefore, Area Blue Circle is;πb²= π(6.25)²= 625π/16 square units.= 122.718463031 sq...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3582512

Calculating perimeter of the blue inscribed square.5² = 7²+8²-2*7*8cosa112cosa = 49+64-25cosa = 88/112a = acos(11/14)a = 38.2132107017°5/sin38.2132107017 = 7/sinbsinb = ⅕(7sin38.2132107017)sinb = 0.86602540378b = asin(0.86602540378)b = 60°c = 180-60c = 120°d = 180-120-38.2132107017d = 21.7867892983°Calculating x, side length of the inscribed blue square.x/sin21.7867892983 = 7/sin120x = (7sin21.7867892983)/(sin120)x = 3 units.There, perimeter of the inscribed blue square is;4xAnd x = 3 units.= 4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3581617

Calculating r, radius of the circle.Let the small inscribed right-angled triangle shortest length be x.3 ~ 4x ~ aCross Multiply.3a = 4xa = ⅓(4x) units.a is the big inscribed right-angled triangle shortest length.b²+x² = 3²b = √(9-x²) units.3 ~ 4√(9-x²) ~ cCross Multiply.3c = 4√(9-x²)c = ⅓(4√(9-x²)) units.It implies;3x = x+c3x = x+⅓(4√(9-x²))9x = 3x+4√(9-x²)6x = 4√(9-x²)3x = 2√(9-x²)9x² = 4(9-x²)9x² = 36-4x²13x² = 36x² = 36/13x = √(36/13)x = 6√(13)/13 units.x = 1.66410058868 units.Recall.a = ⅓(4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3580129

Calculating x.a² = 9a = √(9)a = 3 units.a is the side length of the inscribed square.b² = 3²+3²b² = 2*3²b = √(2*3²)b = 3√(2) units.b is the radius of the half circle.c = 2bc = 2*3√(2)c = 6√(2) units.c is the diameter of the half circle.d² = 3²+(3√(2))²d² = 9+18d = √(27)d = 3√(3) units.It implies;cose = x/(6√(2)) --- (1).cose = 3√(2)/3√(3)cose = √(2)/√(3) --- (2).Equating (1) and (2).x/(6√(2)) = √(2)/√(3)√(3)x = 12x = 12/√(3)x = 4√(3) units.x = 6.92820323028 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3579049

Calculating R, radius of the blue circle.a = (R-2) cm.b = ½(20)b = 10 cm.R, radius of the blue circle is;R² = (R-2)²+10²R² = R²-4R+4+1004R = 104R = 26 cm.

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