Answer:
[tex]\huge\boxed{\sf 8 + 4\sqrt{2} \ cm }[/tex]
Step-by-step explanation:
[tex]\theta = 45 \textdegree[/tex]
opposite = 4 cm
Using tan first to find the adjacent side:
[tex]\displaystyle tan \theta = \frac{opposite}{adjacent} \\\\tan \ 45 = \frac{4}{adjacent}\\\\1 = \frac{4}{adjacent} \\\\Multiply \ 'adjacent' \ to \ both \ sides\\\\adjacent = 4 \ cm[/tex]
Finding Hypotenuse now by using Pythagorean theorem:
[tex](Hyp)^2 = (base)^2 + (perp)^2[/tex]
where base = 4, hyp = 4
(Hyp)² = (4)² + (4)²
(Hyp)² = 16 + 16
(Hyp)² = 32
Take sqrt on both sides
[tex]Hyp = 4\sqrt{2}[/tex] cm
Exact perimeter of triangle:
= base + perpendicular + hypotenuse
= 4 + 4 + 4√2
= [tex]8 + 4\sqrt{2}[/tex] cm
[tex]\rule[225]{225}{2}[/tex]
