Mathematics Question and Solution
Let a be the side length of the big inscribed square.
Let b be the side length of the bigger inscribed square.
Therefore;
27 ~ b
a ~ 64
Cross Multiply.
ab = 27*64
b = (1728)/a units.
Notice.
(a+b) units is the side length of the biggest inscribed square.
a+b = a+(1728)/a
= (a²+1728)/a units.
Calculating a.
((a²+1728)/a)² = ((1728)/a)²+64²
((a⁴+3456a²+2985984)/a²) = (2985984/a²)+4096
a⁴+3456a²+2985984 = 2985984+4096a²
a⁴ = 4096a²-3456a²
a² = 640
a = √(640)
a = 8√(10) units.
It implies (a+b) is;
(a²+1728)/a
And a = 8√(10) units.
= ((8√(10))²+1728)/(8√(10))
= (640+1728)/(8√(10))
= 2368/(8√(10))
= 296/√(10)
= ⅒(296√(10)) units.
It implies;
x, area of the biggest inscribed square is;
x = (a+b)²
x = (⅒(296√(10)))²
x = ⅒(87616) square units.
x = 8761.6 square units.
