SOLUTION: A diagonal drawn through square A is half as long as a diagonal drawn through square B. The area of square B is how many times the area of square A? a 1/4 b 1/2 c 2 d 4

Question 340831: A diagonal drawn through square A is half as long as a diagonal drawn through square B. The area of square B is how many times the area of square A?
a 1/4 b 1/2 c 2 d 4 e 8
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A diagonal drawn through square A is half as long as a diagonal drawn through square B.
The area of square B is how many times the area of square A?
:
Establish the relationship between the diagonal and the area
Let x = the diagonal of square A
Let s = the side of square A
s^2 + s^2 = x^2
= x
= x
s =
Area = s^2
A =
A = the area of A
:
Let 2x = diagonal of B
Replace x with 2x in the above equation
A =
A =
A = is the area of B
:
Divide Area of B by the area of A

2x^2 *
Cancel x^2
2 * 2 = 4 times area of A is the area of B

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