Answer:
Choose all but C
Explanation:
Givens
Area = 182 m^2
Perimeter = 54 m
Solution.
B: solves for the length, not the width. Area = L*w. Area / w = L. But to get to the length, you need to solve for the width. So this statement can be used. B is true.
C is not true. The length and width differ by 1 which means one of them is even and the other is odd. See below under A.
D is also true. 2L = 54 - 2w Divide both sides by 2
2L/2 = 54/2 - 2w/2
L = 27 - w
E is true.
L * w = 182 Divide both sides by w
L = 182/w
The only one we don't know about is A. We have to solve the problem to get the answer to A.
P= 2L + 2w = 54
2L + 2w = 54
L + w = 27
L = 27 - w
L*w = 182
(27 - w ) * w = 182 Remove the brackets
27w - w^2 = 182 Subtract 27w - w^2 from both sides.
0 = w^2 - 27w + 182 Notice the sign change. Subtraction does that.
This factors into
(w - 13)(w - 14)
A turns out to be true, because w can be 13 or 14. When W = 13, L = 14.
When w = 14, L = 13