We are given a right angle.
Two of the sides are 5sqrt(2)cm and 3cm.
We need to find the length of third side x.
We know, we can apply Pythagoras Theorem for a right triangle.
(a)^2 +(b)^2 =(c)^2.
Where, a and d b are two smaller sides of the right triangle and c is the longest side (Hypotenuse) of the right triangle.
Plugging values in above formula, we get
(x)^2 +(3)^2 = [tex](5\sqrt{2})^2[/tex]
x^2 +9 = 25*2
x^2+9 =50
Subtracting 9 from both sides, we get
x^2+9-9 =50-9
x^2 = 41.
Taking square root on both sides, we get
[tex]\sqrt{(x)^2}=\sqrt{41}[/tex]
[tex]\sqrt{41}[/tex] can't be simplify more.
Therefore, final answer is x= [tex]\sqrt{41}[/tex] cm.
