Carcass wrote:
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 values of y?
A. \(y > \sqrt {2}\)
B. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)
C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)
D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)
E. \(y < \frac {\sqrt {3}}{4}\)
There are infinitely many right triangles that have an area of 1.
So, one approach is to find a triangle that meets the given conditions, and see what conclusions we can draw.
Here's one such right triangle:
This meets the conditions that the area is 1 AND x < y < z
With this triangle, y = 4
When we check the answer choices, only one (answer choice A) allows for y to equal 4
Answer: A
Cheers,
Brent