Before we get started, make sure you remember Monday’s Brain Twister!
Right triangle DEF has a hypotenuse of less than 7. What is the maximum possible area of DEF, if the area of DEF is an integer?
Numeric Entry: [_____________]
Answer and Explanation
To maximize the area of a right triangle, we must assume that the triangle is a 45:45:90. Now, we don’t know if this will lead to an integer area, but it is a good first line of attack.
Using the Pythagorean theorem, we know that . The hypotenuse squared must be less than , so 48 is a good place to start. If the hypotenuse squared is 48, then we can do the following:
Area of 45:45:90 triangle is , which equals .
How’d you do?