My Negative Contrast Area

Geometry Level 1

A B C D ABCD is a square with an area of 225.
The black region consists of edges that are parallel to the sides of the square.
What is the perimeter of the black region?


The answer is 60.

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3 solutions

The length of side of the square is 225 = 15 \sqrt{225}=15 . Observed that the length C D CD is the sum of the lengths of the horizontal sides of the black rectangles and the length B C BC is the sum of the lengths of the vertical sides of the black rectangles. That's why the perimeter of the black region is 15 + 15 + 15 + 15 = 15+15+15+15= 60 \color{#D61F06}\boxed{\large 60}

Sam Bealing
May 8, 2016

225 = 15 \sqrt{225}=15 so the square has side length 15 15

Consider the vertical perimeter of the region. On one side we have the side of the square that has length 15 15 . The vertical side length on the other side is just the side of the square split up so also has length 15 15 .

We have a similar result for the horizontal perimeter so our overall perimeter is:

15 × 4 = 60 15 \times 4=\boxed{60}

Moderator note:

Good observation about the perimeter of such a figure. If we wanted to calculate the perimeter, it often helps to move the sides.

Alex Wang
Aug 1, 2017

Move the black edges to the side. Then it is obvious that the perimeter is 60 since sqrt(225)=15 15*4=60

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