Perimeters Provided Around In The Vicinity Of Its Perimeter

Geometry Level 1

The rectangle A B C D ABCD was divided into 9 small rectangles, and some rectangles have their perimeter inside it. The perimeter of rectangle A B C D ABCD is 54 cm 54 \text{ cm} . What is the perimeter of the gray rectangle?

15 19 20 22 24

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Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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5 solutions

Relevant wiki: Length and Area Problem Solving

13 Helpful 0 Interesting 0 Brilliant 0 Confused

Whole lot of work for the simplex factuur that for every given rectangle 3 out of 4 sides give the perimeter of ABCD. So 74 - 54 = 20

Peter van der Linden - 4 years, 11 months ago

37-27=10 ;-) So b + e = 10 and then gray perimeter = 2*10 = 20.

Manu Silva - 4 years, 9 months ago

where did you get 37 from?

Matthew Agona - 4 years, 9 months ago

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If you add all the 4 equations up, from i-iv, a+2b+c+d+2e+f=37

A Former Brilliant Member - 4 years, 9 months ago

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ahhh. foolish me. thanks!

Matthew Agona - 4 years, 9 months ago

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@Matthew Agona – oops I meant t say 4 equations, from i-iv

A Former Brilliant Member - 4 years, 9 months ago

using your way .. 2a+2b+2c+2d+2e+2f=54 =>>#1 b+d+a+e+c+e+b+f=8+9+7+13=37 then a+2b+c+d+2e+f=37 =>>#2 2b+2e=37-(a+c+d+f) =>>#3

1-#2

a+c+d+f=17 =>> in #3 2b+2e=37-(17)=20 2(b+e)=20 the perimeter of the gray rectangle equals 2(b+e)=20 CM

Abt HN - 4 years, 9 months ago
汶良 林
Sep 3, 2016

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Exactly. Sum the perimeters of the four rectangles (74), and subtract the known perimeter of ABCD.

Andy Boal - 4 years, 8 months ago
Giuseppe Nocera
Jul 19, 2016

The sum of the perimeters of the 4 rectangles is equal to the sum between the perimeter of ABCD rectangle and the grey one

6 Helpful 0 Interesting 0 Brilliant 0 Confused

You probably meant that, but the sum of the 4 rectangles is equal to the SUM of the perimeter of ABCD and the grey area.

Kai Ott - 4 years, 11 months ago

Quella è l'area

Gabriele Bellavia - 4 years, 11 months ago
Venkatachalam J
Feb 15, 2017

Relevant wiki: Length and Area Problem Solving

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Elie Hage Moussa
Jul 31, 2016

The empty sub-rectangles perimeters are : 14 (54-26-14), 10 (54-18-26), 24 (54-16-14), 20 (54-18-16).

There are 3x3 sub-rectangles, Thus, 3x54 = sum(perimeter(sub-rectangles)) Gray perimeter = 3*54-14-16-18-26-14-10-24-20=20

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