SAT question

Geometry Level 2

A square is inscribed inside another square. The lengths are recorded.

Let A = b 2 9 a 2 A = \frac{b^2}{9a^2} , and B = 2 3 B =\frac{2}{3} .

Determine which is greater, A A or B B ?

B = A B = A B > A B > A B < A B < A The relationship can not be determined

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Zach Bian
Dec 29, 2017

From any of the right triangles: a 2 + ( 2 a ) 2 = b 2 a^2+(2a)^2=b^2

5 a 2 = b 2 5a^2=b^2

Quantity A = 5 / 9 5/9

Quantity B = 6 / 9 6/9

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you for sharing your solution.

Hana Wehbi - 3 years, 5 months ago

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