Mathematics Question and Solution
Sir Beg is the author of the question.
Notice.
The composite plane shape is not drawn to scale.
2a² = 2²
a² = 2
a = √(2) cm.
a is OC = AC.
2b² = √(2)²
b² = 1
b = 1 cm.
b is OF = CF = DE, the length of the inscribed rectangle CDEF.
Calculating EF = CD, the width of the inscribed rectangle CDEF.
Let it be d.
c = (1+d) cm.
It implies;
2² = 1+(1+d)²
4 = 1+1+2d+d²
d²+2d-2 = 0
(d+1)² = 2+1²
d = -1±√(3)
Therefore;
d = (√(3)-1) cm.
d = 0.7320508076 cm.
Again, d is EF = CD, the width of the inscribed rectangle CDEF.
Area triangle CDEF is;
bd
= 1*(√(3)-1)
= (√(3)-1) cm²
= 0.7320508076 cm²
= d cm²
