Question

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

Answer 1

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

Explanation:

Given the perimeter of the triangle = 43 feet

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

shortest side =
`(1)/(3)` x a

=
`(a)/(3)` feet

longest side = (4 x
`(a)/(3)`) + 3

=
`(4a)/(3)` + 3

Perimeter = a +
`(a)/(3)` + (
`(4a)/(3)` + 3)

⇒ 43 = a +
`(a)/(3)` +
`(4a)/(3)` + 3

43 - 3 = a +
`(a)/(3)` +
`(4a)/(3)`

40 =
`(3a+a+4a)/(3)`

=
`(8a)/(3)`

40 x 3 = 8a

120 = 8a

a =
`(120)/(8)`

= 15

Therefore,

middle side = 15 feet

shorter side =
`(a)/(3)` =
`(15)/(3)`

= 5 feet

longest side = (4 x
`(a)/(3)`) + 3

= (4 x 5) + 3

= 23 feet