According to Pythagorean theorem,
Δ (Hypotenuse)² = (1st Leg)² + (2nd Leg)²
⇒ (x + 8)² = x² + 12²
⇒ x² + 64 + 16x = x² + 144
⇒ 16x = 80
⇒ x = 5
Hypotenuse = (x + 8) = (5 + 8) = 13
1st Leg = 5
2nd Leg = 12
We know that : Perimeter is the Sum of all sides of the Triangle
⇒ Perimeter = Hypotenuse + 1st Leg + 2nd Leg
⇒ Perimeter = 13 + 5 + 12
⇒ Perimeter = 30
We know that :
[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]
Base = 1st Leg
Height = 2nd Leg
[tex]\implies \sf{\textsf{Area of the Triangle} = \dfrac{1}{2} \times 5 \times 12}[/tex]
[tex]\implies \sf{\textsf{Area of the Triangle} = 30}[/tex]
