Mathematics Question and Solution
Calculating Area of the Red Rectangle.
Let x and y be the length and width of the red rectangle respectively.
tana = 4/3
a = atan(4/3)°
b = 90-a
b = atan(3/4)°
c = ½(180-a)
c = ½(180-atan(4/3))°
d = ½(180-b)
d = ½(180-atan(3/4))°
tan(½(180-atan(4/3))) = 3/e
e = 3/tan(½(180-atan(4/3)))
e = ½(3)
e = (3/2) units.
tan(½(180-atan(3/4))) = 4/f
f = 4/tan(½(180-atan(3/4)))
f = ⅓(4)
f = (4/3) units.
Therefore;
x = 4+(4/3)
x = ⅓(16) units.
Again, x is the length of the red rectangle.
y = 3+(3/2)
y = ½(9) units.
Again, y is the width of the red rectangle.
It implies, area green rectangle is;
xy
= ⅓(16)*½(9)
= 8*3
= 24 square units.
Or
Calculating Area of the Red Rectangle.
Let x and y be the length and width of the red rectangle respectively.
a² = 2(3)²
a = 3√(2) units.
b² = 2(4)²
b = 4√(2) units.
c = a+b
c = 3√(2)+4√(2)
c = 7√(2) units.
d = 4-3
d = 1 unit.
cose = d/c
e = acos(1/(7√(2)))°
e = 84.2023636705°
f = e-45
f = 84.2023636705-45
f = 39.2023636705°
g = 90-f
g = 90-39.2023636705
g = 50.7976363295°
h = ½(180-f)
h = 0.5(180-39.2023636705°)
h = 70.3988181648°
j = ½(180-g)
j = 0.5(180-50.7976363295)
j = 64.6011818353°
tanh = 4/k
tan70.3988181648 = 4/k
k = 1.4244289009 units.
tanj = 3/l
tan64.6011818353 = 3/l
l = 1.42442890089 units.
Notice.
k = l
Therefore;
x = 4+k
x = 4+1.42442890089
x = 5.42442890089 units.
Again, x is the length of the red rectangle.
y = 3+l
y = 3+1.42442890089
y = 4.42442890089 units.
It implies, area red rectangle is;
xy
= 5.42442890089*4.42442890089
= 24 square units.
Or
Calculating Area of the Red Rectangle.
Let x and y be the length and width of the red rectangle respectively.
a² = 2(3)²
a = 3√(2) units.
b² = 2(4)²
b = 4√(2) units.
c = a+b
c = 3√(2)+4√(2)
c = 7√(2) units.
d = 4-3
d = 1 unit.
e² +1² = (7√(2))²
e² = 98-1
e = √(97) units.
f = (z+4) units.
Where f = x.
g = (z+3) units.
Where g = y.
h = e-z-z
h = (√(97)-2z) units.
Calculating z.
f²+g² = h²
(z+4)²+(z+3)² = (√(97)-2z)²
z²+8z+16+z²+6z+9 = 97-4√(97)z+4z²
2z²+14z+25 = 97-4√(97)z+4z²
2z²-53.3954312072z+72 = 0
Therefore;
z ≠ 25.274 units.
z = 1.424 units.
Recall.
f = (z+4) units.
And f = x, z = 1.424 units.
x = 1.424+4
x = 5.424 units.
g = (z+3) units.
And g = y, z = 1.424 units.
y = 1.424+3
y = 4.424 units.
It implies;
Area Red Rectangle is;
xy
= 5.424*4.424
= 24 square units.
