Carcass wrote:
Quantity A |
Quantity B |
The length of a leg of an isosceles right triangle with area R |
The length of a side of a square with area R |
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.
The length of a leg of an isosceles right triangle with area RLet x = the length of one legSince this is an
isosceles right triangle, the length of the other leg must also be x
Also, since this is a
right triangle, then the base has length x AND the height is x
Area of triangle = (base)(height)/2
So, we can write: R = (x)(x)/2
Simplify: R = x²/2
Multiply both sides by 2 to get: 2R = x²
Take square root of both sides to get: √(2R) = x
Great, we have now written Quantity A in terms of R
The length of a side of a square with area RLet y = the length of one side of squareSo, we can write: R = (y)(y)
Simplify: R = y²
Take square root of both sides to get: √R = y
We have now written Quantity B in terms of R
So, we now have the following:
Quantity A: √(2R)
Quantity B: √R
At this point, we may recognize that Quantity A is greater.
However, if you need more convincing, we can take √(2R) and REWRITE it as (√2)(√R) to get:
Quantity A: (√2)(√R)
Quantity B: √R
Now divide both quantities by √R to get:
Quantity A: √2
Quantity B: 1
Since √2 ≈ 1.4, we can see that Quantity A is greater
Answer: A
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep