Answer:
[tex]x=14[/tex]
Step-by-step explanation:
Considering the small triangle in which the one side and two angles are given:
Finding the third angle of the small triangle
Sum of angles of the triangle is [tex]180[/tex]°
as two angles are given i.e 90° and 45°, so third angle is 180°-(90°+45°)
Third angle in the small triangle is 45°.
As the opposite angles are 45° joining together to form 90° angle, therefore the small triangle is an isosceles triangle in which the opposite sides are equal.
Therefore the two sides are 7 and 7 of small triangle, so By Pythagoras theorem the third side is
[tex]H=\sqrt{P^2+B^2}\\ \\=\sqrt{7^2+7^2}\\\\=\sqrt{98} \\H=7\sqrt{2}[/tex]
Similarly the bigger triangle is also an isosceles triangle whose base is determined i.e [tex]7\sqrt{2}[/tex] = perpendicular length of bigger triangle.
Applying the Pythagoras theorem in bigger triangle:
[tex]x=\sqrt{(7\sqrt{2})^2+(7\sqrt{2})^2 }\\x=\sqrt{98+98}\\\\ x=\sqrt{196} \\\\x=14[/tex]
