+389 A square region with perimeter 60 inches is made with square inch tiles. Bob removes one tile from the square and rearranges the remaining tiles without any overlap to make a rectangular region with minimum perimeter. How many inches are in the perimeter?
+14903 Hallo dabae!
A square region with perimeter 60 inches is made with square inch tiles. Bob removes one tile from the square and rearranges the remaining tiles without any overlap to make a rectangular region with minimum perimeter. How many inches are in the perimeter?
The side length of the square
a = P / 4 = 60 inch / 4
a = 15 inch
Is the area of the square
A1 = a² = (15 inch)²
A1 = 225 sqin
The new surface is
A2 = 225sqin - 1sqin
A2 = 224 sqin
The shortest side would
a(min) = √224sqin
a(min) = 14,97inch
224sqin = 225sqin - 1sqin = (15inch)² - 1sqin = (15 +1)inch * (15 - 1)inch = 16inch * 14inch
The corresponding integer side lengths (a * b = 224sqin) are
a = 14 inch
b = 16 inch
The scope of the rectangular area
P = 2a + 2b = 2 * (14 + 16) inch
P = 60 inch
Greetings asinus 
:- )
+14903 Hallo dabae!
A square region with perimeter 60 inches is made with square inch tiles. Bob removes one tile from the square and rearranges the remaining tiles without any overlap to make a rectangular region with minimum perimeter. How many inches are in the perimeter?
The side length of the square
a = P / 4 = 60 inch / 4
a = 15 inch
Is the area of the square
A1 = a² = (15 inch)²
A1 = 225 sqin
The new surface is
A2 = 225sqin - 1sqin
A2 = 224 sqin
The shortest side would
a(min) = √224sqin
a(min) = 14,97inch
224sqin = 225sqin - 1sqin = (15inch)² - 1sqin = (15 +1)inch * (15 - 1)inch = 16inch * 14inch
The corresponding integer side lengths (a * b = 224sqin) are
a = 14 inch
b = 16 inch
The scope of the rectangular area
P = 2a + 2b = 2 * (14 + 16) inch
P = 60 inch
Greetings asinus :- )
