Mathematics Question and Solution
Observing similar plane shape side lengths ratio.
3 - 5
a - (4-a)
Cross Multiply.
3(4-a) = 5a
12-3a = 5a
8a = 12
a = 3/2 units.
a is the base of the right-angled triangle with height 3 units.
b = 4-a
b = 4-(3/2)
b = 5/2 units.
b is the base of the right-angled triangle with height 5 units.
c² = 3²+(3/2)²
c² = 9+(9/4)
c² = ¼(45)
c = ½√(45) units.
d² = 5²+(5/2)²
d² = 25+(25/4)
d² = ¼(125)
d = ½√(125) units.
e = c+d
e = ½√(45)+½√(125)
e = (3/2)√(5)+(5/2)√(5)
e = 4√(5) units.
e is the hypotenuse of the right-angled triangle with adjacent sides 3 units and x unit respectively.
Calculating x.
It implies;
e² = 3²+x²
(4√(5))² = 9+x²
80 = 9+x²
x² = 80-9
x² = 71
x = √(71) units.
