A. i am a rectangle

B. my dimensions are concesutive counting numbers

C. the sum of my length and width is a prime number

D. my perimeter is 3 less than a prime number and 1 more than another prime number

E. my area is not a square number

F. my area is less than 100 and greater than 64

assuming the sides are a and b

b = a+1 from B

from F, a(a+1) > 64 and a(a+1) < 100, which gives the values of a as 8 or 9

if a = 8, b = 9, a+b = 17

if a = 9, b = 10, ,a+b = 19

both satisfy contraints C

if a = 8 b = 9, perimeter is 34 which is 37-3 and 33+1, howeve 33 is not a prime

so the answer is a = 9, and b = 10

the perimeter is 38 which is 37+1 and 41 - 3, both 37 and 41 are primes (contraint D)
by Level 3 User (2.1k points)
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No one posted an answer to this question. What is the answer?

A and B: length=X and width=X+1.

C: 2X+1 is prime.

D: perimeter=4X+2=p1-3 and p2+1 where p1 and p2 are prime.

E and F: X(X+1)=X^2+X cannot be prime and 64<X(X+1)<100.

X^2+X-64>0; X^2+X-100<0; X^2+X+1/4>64.25; (X+1/2)^2>64.25, so X>7.51; (X+1/2)^2<100.25, so X<9.51. If X is a whole number, it must be 8 or 9. Both satisfy C. 4X+5 is 37 or 41. 4X+1 is 33 or 37. Since 37 is prime, X=9. The dimensions of the rectangle are 9 and 10 with perimeter 38.

Check list:

A and B: length=9 width=10.

C: 19.

D: 38 is 3 less than 41 and 1 more than 37.

E: 90 is not a perfect square.

F: Area=90 is between 64 and 100.

by Top Rated User (711k points)