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danica has laid out floor tiles so they form a rectangle with a perimeter of 18 inches. what is the difference between the greatest and least possible areas of the rectangle

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gwendolyn555

Least: 8 (length) x 1 (width) = 8
Greatest: 5 (length) x 4 (width) = 20
Difference: 20 - 8 = 12

Answer:

Difference between the greatest and least possible areas of the rectangle = 20-8 = 12 inches.

Step-by-step explanation:

Let Length be denoted by L

and Breadth be denoted by B

then , Perimeter of rectangle is given by 2\(\times\)(L+B)

Given - Perimeter of rectangle be 18 inches.

2\(\times\)(L+B) = 18

L+B = 9

find the possible pairs of integers such that the sum of integers is 9

So, possible pairs arises are - 8,1 ; 7,2 ; 6,3 ; 5,4

Area of rectangle = Length  \(\times\) Breadth = L\(\times\)B

finding area for each pair

8\(\times\)1 = 8

7\(\times\)2= 14

6\(\times\)3= 18

5\(\times\)4= 20

So , the greatest possible area is 20 inches and least possible area is 8 inches.

Thus, Difference between the greatest and least possible areas of the rectangle = 20-8 = 12 inches.

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