Mathematics Question and Solution
Calculating MC ÷ DM.
Notice.
140 cm² is the area of the the ascribed rectangle.
Let x be the length.
xy = 140
y = 140/x cm.
y is the width of the rectangle.
½*a*x = 38
ax = 76
a = 76/x cm.
a is the height of the green inscribed triangle area.
½*b*y = 46
by = 92
And y = 140/x cm.
b(140/x) = 92
70b = 46x
b = 46x/70 cm.
b is the height of the yellow inscribed triangle.
c = 2a
c = 2(76/x)
c = 152/x units.
c is y, the width of the ascribed rectangle.
d = a+b
d = ((76/x)+(46x/70))
d is x, the length of the ascribed rectangle.
Calculating x.
((76/x)+(46x/70)) = x
5320+46x² = 70x²
5320 = 24x²
x = √(5320/24)
x = 14.8884742894 cm.
Again, x is the length of the ascribed rectangle.
Recall.
y = 140/x
And x = 14.8884742894 cm.
y = 140/14.8884742894
y = 9.40324691963 cm.
y is the width of the ascribed rectangle.
Notice.
AD = DM.
And AD = y = 9.40324691963 cm.
Therefore;
DM = 9.40324691963 cm.
It implies;
DM+MC = x
9.40324691963+ MC = 14.8884742894
MC= 14.8884742894-9.40324691963
CM = 5.48522736977 cm.
Therefore, MC ÷ DM is;
5.48522736977/9.40324691963
= 0.58333333333
= 7/12
