Question

what is the perimeter, in feet (ft), of a right triangle which has an area of 12 ft^2 and one leg that has a length of 4 ft?

Answer 1

Answer:

           P = (10 + 2√13) ft ≈ 17.21 ft

Step-by-step explanation:

A = 12 ft²     - area of triangle

a = 4 ft, b    - legs of right triangle

c       - hypotenuse (third side of triangle)

A = ¹/₂ ab

12 =  ¹/₂•4•b

12 = 2b

b = 6 ft

from Pythagorean theorem:

a² + b² = c²

4² + 6² = c²

c² = 16 + 36

c = √52 = 2√13 ft

The perimeter:  P = a + b + c

P = 4 + 6 + 2√13 = (10 + 2√13) ft ≈ 10 + 7.21 = 17.21 ft