Question #157 Quant. Review

[GHong14]

A certain right triangle has sides of length x, y, and z, where x<y<z. if the area of this triangular region is 1, which of the following indicates all of the possible value of y.

a. y > sqt (2)
b. sqt(3)/2 < y < sqt (2)
c. sqt(2)/3 < y < sqt (3)/2
d. sqt(3)/4 < y< sqt (2)/3
e. y < sqt (3)/4

correct answer is A

Can anyone elaborate?

[kevincanspain]

A certain right triangle has sides of length x, y, and z, where x<y<z. if the area of this triangular region is 1, which of the following indicates all of the possible value of y.

a. y > sqt (2)
b. sqt(3)/2 < y < sqt (2)
c. sqt(2)/3 < y < sqt (3)/2
d. sqt(3)/4 < y< sqt (2)/3
e. y < sqt (3)/4

correct answer is A

Can anyone elaborate?

The area of this right triangle is xy/2, so xy=2
Since x< y, xy < y^2
Thus y^2 > 2 and y > sqrt(2)

Alternatively, look at any example: x=1 , y=2 and choose the answer choice consistent with this example : A