Mathematics Question and Solution
Let AD = CD = a.
Calculating a.
b² = 2a²
b = √(2)a units.
b is AC.
c²+3² = a²
c = √(a²-9) units.
c is DE.
a² = d²+7²
d = √(a²-49) units.
e = c-d
e = (√(a²-9)-√(a²-49)) units.
e is CB.
It implies;
b² = e²+10²
(√(2)a)² = (√(a²-9)-√(a²-49))²+100
2a² = a²-9-2√((a²-9)(a²-49))+a²-49+100
2√((a²-9)(a²-49)) = 42
√((a²-9)(a²-49)) = 21
(a²-9)(a²-49) = 441
a⁴-49a²-9a²+441 = 441
a⁴-58a² = 0
a² = 58
a = √(58) units.
Therefore, Orange Area is;
½(a²)
= ½*√(58)²
= ½*58
= 29 square units.
