Right triangle DEF has sides that measure x, x, and x squared for the some value of x. What is the area of triangle DEF to the nearest 0.1 square unit?
If it is right-angled, then
x^2 + x^2 = (x^2)^2
x^4 - 2x^2 = 0
x^2(x^2 - 2) = 0
x = 0 , which is no good
or
x^2 = 2
x = √2
then the area = (1/2)(x)(x) = 1/2 (√2)^2
= (1/2)(2)
= 1 square unit