# In triangle 45, 45, 90 DEF triangle, angle D is congruent to angle F. The perimeter of triangle DEF is 35 mm, and DF = 14mm, how do you determine DE?

##### 1 Answer

There are a few ways to go about solving this, but this problem is incorrect in its statements.

A 45, 45, 90 triangle is isosceles by definition, so its two legs have equal length. Because it is given that

Side DE could be expressed easily as

However, the triangle's perimeter in this case wouldn't be 35. That's where the problem is wrong. When working with radicals your answer will hardly ever be rational. If you use this method, the triangle's perimeter is