Question

A right-angled triangle has a hypotenuse of length 2 + √2 and one other side of length 1+√2. Find the length of the third side and the area, expressing each answer as a surd in its simplest form.​

Answer 1

2.4 units

Explanation:

r^2=x^2 + y^2 ....(theorem of Pythagoras)

(2+√2)^2=(1+√2)^2 + x^2

6+4√2=(3+2√2)+x^2

6+4√2-3-2√2=x^2

√3+2√2=√x^2

2.4 units = x