the perimeter of a triangle is 43 ft. The shortest side is one-third the length of the middle side. The longest side is 3 feet more than four times the shortest side. Find the lenghts of the three sides

shorter side = 5 feet, middle side = 15 feet, and longest side = 23 feet

Step-by-step explanation:

Given the perimeter of the triangle = 43 feet

Let the length of the middle side be represented by a. Then;

shortest side = x a

                     = feet

longest side = (4 x ) + 3

                    = + 3

Perimeter = a + + ( + 3)

⇒ 43 = a + + + 3

43 - 3 = a + +

40 =

    =

40 x 3 = 8a

120 = 8a

a =

  = 15

Therefore,

middle side = 15 feet

shorter side = =

                    = 5 feet

longest side = (4 x ) + 3

                    =  (4 x 5) + 3

                    = 23 feet

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%