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Geometry Level 3

There are 5 squares.

The area of the green squares are 34 and 74. The area of the 2nd orange square is 25.

Which colored area has more area in square units?

Notation: You don't actually need to know the area of some of the squares to solve this problem. It just makes the problem easier.

This is part of the series called " It's easy, believe me! "

The area colored green. They have the same area. Cannot be determined. The area colored orange.

2 solutions

Marco Brezzi
Aug 17, 2017

Since $a$ and $b$ are congruent, if we constructed a square on the lower side of $b$ , it would have the same area of $A$ . Thus, by the Pythagorean theorem

$A_B=A_A+A_C$

With a similar reasoning

$A_D=A_C+A_E$

Hence

$\text{Green area} =A_B+A_D=A_A+A_E+2A_C$

$\text{Orange area} =A_A+A_C+A_E$

Therefore, provided that $C$ has non-zero area, the green area is larger

why $a$ and $b$ are congruent?

s p - 3 years ago

Abha Vishwakarma
Sep 1, 2018

The triangles formed are congruent and right angled. So using Pythagoras theorem, A + 25 = 34 and B + 25 = 74. Since the total area of the green region has two times the area of the second square hence the green region has a larger area. (Though at first, my mind tricked me to think it was the other way :-P)

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