My approach:
To calculate the rectangle area, we need to get its sides' measures. Let's say the two sides are: a and b, and the diagonal is d. a,b,d form a right triangle.
As a and b can be substitute for each other, I'll consider the relationship between a and d only.
For example
d is 5, one side of the rectangle is 4, what is the area of it?. If a = 4 then b = 3, if a = 3 then b = 4, however, the product a*b is unchanged. So I just take a = 4, the a = 3 is the reversal version ( when b takes the position of a to be 4).
1. d^2 = a^2 + b^2,
and d = 2a
We have no measure here, just the ratio. So we can only figure out the ratio d
b with such given information.
Insuff.
2. d^2 = a^2 + b^2
and d = a + 0.1
Plug in d = a+0.1 into the equation:
(a + 0.1)^2 = a^2 + b^2 => 1 equation, 2 unknowns, we can only get a relationship between a and b
or a = f(b) or b = f(a)
Insuff.
1&2.
Given information:
d = 2a
d = a +0.1 or d = b + 0.1
d = 2a gives us the shape of the triangle, the ratio among a,b,d is fixed.
The shape has been fixed, now we can zoom up or zoom down the triangle to let:
either d = a + 0.1
or d = b + 0.1
Thus, we have two different sets of value, so the area of the rectangle can have 2 different possible values
To make it clearer take this example:
The ratio of d to one side of the triangle is 5/3,
d is 2 units longer than 1 one side, what is the area of the triangle?
You may first think of : 5,3,4 as a set of value ( 5 - 3 = 2)
However, 10,6,8 also a possible set of value ( 10 - 8 = 2)
The first area = 3*4 /2 = 6
The second = 6*8/2 = 24
Now, you get what I mean.
1&2 is also insuff.
Pick E.
Please cite the source and OA's explanation for C.
"There is nothing either good or bad - but thinking makes it so" - Shakespeare.
b with such given information.
