Square - Squares

Geometry Level 1

Starting with a square piece of paper that measures 20 inches by 20 inches, Calvin cuts out a 5 inch by 5 inch square from each of the 4 corners. What is the perimeter of the resulting shape?

40 80 100 120

3 solutions

Nelvson Shine
Jul 29, 2013

say that the square piece of paper called square ABCD.

AB = CD = BC = AD

= AB $\times$ 4

"Calvin cuts out a 5 inch by 5 inch square from each of the 4 corners. "

say that in AB line, Calvin cuts both left and right side, so AB line is $20 - 5 - 5 = 10 inch$

that cuts, leave a 5 inch square, 2 in the left side, and 2 in the right side.

since in a square there is 4 side, the perimeter of the resulting shape is =

$(4 \times 10) + ( (5+5) \times 4)$

$= 40 + 40 = 80$

Thus the answer is 80

Jose Mateos
Jul 29, 2013

The perimeter of the square is 80 ( $20 \times 2 + 20 \times 2$ ) When we are cutting these little squares, the perimeter we are taking is being increased in the other two sides of the square (I know that it may sound weird, but I can't explain better without any images), so the perimeter remains equal.

Moderator note:

Interesting idea that "the perimeter remains equal". Is this true no matter where the 5 inch square is cut? Would the answer be the same if the cuts were made in the middle of the larger square, instead of the corners?

Of course it isn't the same. When you cut the corners, you are "moving" a segment that you are putting in the opposite side of the square, so you are subtracting 5 and adding 5, so it remains equal. If you cut in the middle you are increasing the perimter by 10, because there are two segments who have been "created".

Jose Mateos - 7 years, 10 months ago

Souperman Arcena
Jul 29, 2013

so each side measures 20-10= 10 then the other side obviously measures 5 so: 10x4=40 5x8=40 40+40=80

Square - Squares

3 solutions

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