Mathematics Question and Solution
Let a be the side length of the purple inscribed square.
b² = 4
b = 2 cm.
b is the side length of the green inscribed square.
c² = 1
c = 1 cm.
c is the side length of the yellow ascribed square.
d = a-c
d = (a-1) cm.
e = a-b
e = (a-2) cm
Calculating a, side length of the inscribed purple square.
Considering similar plane shapes (right-angled triangle) side length ratios.
d - 2
1 - e
It implies;
(a-1) - 2
1 - (a-2)
Cross Multiply.
(a-1)(a-2) = 2
a²-3a+2 = 2
a²-3a = 0
a = 3 cm.
Therefore, area purple inscribed square is;
a²
= 3²
= 9 cm²
