Question

The largest side of a triangle is 3 more than twice the smallest side. The third side is 8 more than the smallest side. What are the lengths of each side if the perimeter is 33?

Answer 1

`14, 5 1/2 and 13 1/2`

Explanation:

Let say `x` is a smallest side.

Therefore,
`(2x+3)+(x)+(x+8)=33`
`4x+11=33`
`4x=33-11`
`x=22/4=11/2`

Therefore the length of each sides are `(2(11/2)+3), (11/2), and (11/2+8)`

`(22/2+6/2),(11/2), and (11/2+16/2)`
`28/2=14, 11/2, and 27/2`

`14, 5 1/2 and 13 1/2`

to check it,

`11/2+28/2+27/2=66/2=33`

Answer 2

The sides of the triangle are `5.5,13.5,14` units each.

Explanation:

Let `s_1 , s_2,s_3` are the smallest,middle and largest side
of the triangle respectively.
By condition given , `s_1 + s_2 +s_3 =33 ; s_3=2s_1+3 ; s_2=s_1+8`
`:. s_1+(s_1+8) +(2s_1+3)=33 or 4s_1+11=33 or 4s_1=22 or s_1=22/4=5.5 :. s_2=5.5+8=13.5 ; s_3=2*5.5+3=11+3=14`

The sides of the triangle are `5.5,13.5,14` units each. [Ans]