Square Trisection

Geometry Level 1

A square is divided into three congruent rectangles. The area of one rectangle is 1200 units. What is the perimeter of the square?


The answer is 240.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Sam Gilbert
Nov 28, 2016

Since all of the rectangles are of equal area, the area of the square is 3600.
Taking the square root of this, we get the side length of the square is 60.
A square has four congruent sides, so the perimeter is 240.

10 Helpful 0 Interesting 0 Brilliant 0 Confused

Calculating the area all at once is a nice short approach to this problem!

I bet several people started off with "Length is l l and Breadth is b b " to set up the equation.

Calvin Lin Staff - 4 years, 6 months ago

How comes?you should specify, according to your solution it is not a rectangle, it is a square

Amer Hamed - 4 years, 6 months ago

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Are you confusing the large square with the 3 small rectangles that it is divided into?

Calvin Lin Staff - 4 years, 6 months ago
Venkatachalam J
Dec 27, 2016

Let the length of the given rectangle is "l" and breadth of the rectangle is "b"

By looking the image we can say that b=l/3

Area of the given rectangle=l*b=l * l/3=1200

l^2=3600=> l=60

b=60/3=20

Therefore the perimeter of the square=2(60+(20+20+20))=2(60+60)=240

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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