Carcass wrote:
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Q and T are the midpoints of opposite sides of square \(PRSU\)
Quantity A |
Quantity B |
The area of region \(PQST\) |
\(\frac{3}{2}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Join QT and say this side as x.
Now say ST as y
we have right angled triangle QTS = ( \(\sqrt{5}\))^2 = x^2+ y^2.
Trick here is that x and y have to be only positive can't be negative.
x^2+ y^2 = 5.
Let's take the combination value.
when x = 2 and y = 1 , this satisfies the equation.
when y = 2 and x = 1 , this satisfies the equation and I don't think any values are possible apart from this.
To get area of QSTP = 1/2 ( xy ) + 1/2 ( xy) = xy.
What ever the value of xy from above we finally get as 2. This value is greater than 1.5
When we consider x and y as \(\sqrt{2}\) and \(\sqrt{3}\) or vice versa,
xy value is greater than 1.5
So answer A.
Hope this is clear.
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