Question

Use the Pythagorean theorem and the following diagram to help you find the area and perimeter of the following triangle. Please show your work and steps, so partial credit may be given:

Answer 1

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 :

`\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : (1)/(2) * Base * Height}}`

Base = 1st Leg

Height = 2nd Leg

`\implies \sf{\textsf{Area of the Triangle} = (1)/(2) * 5 * 12}`

`\implies \sf{\textsf{Area of the Triangle} = 30}`

Answer 2

Perimeter = 30

Area = 30

Explanation:

`(x+8)^2 -x^2 = 12^2`

`x^2 +16x +64 - x^2 = 144`

`16x+64=144`

`16x = 80`

`x = 5`

Double check:

`√(12^2 + 5^2) = (5+8)\\√(12^2 + 5^2) = 13\\13 = 13`

Perimeter:

`12+5+13=30`

Area(
`(1)/(2)bh`):

`(1)/(2)` × 12 × 5 = 30