Question

The first side of a triangle is 4 inches longer then twice th second side the third side of a trianhle

Answer 1

Question:

The first side of a triangle is four inches longer than twice the

second side. The third side of the triangle is 5 inches shorter than

the sum of the other two sides. The perimeter is 72 inches. Find

the lengths of the three sides.

Answer:

The sides of the triangle are: 11.5, 27 and 33.5

Explanation:

Let the first side be f, the second be s and the third be t.

So, we have:

`f =4 + 2s`

`t = f + s - 5`

`Perimeter = 72`

Required

Determine the length of the three sides

Perimeter is calculated as:

`Perimeter = f + t + s`

Substitute values for f and t

`Perimeter = 4+2s + f+s-5 + s`

`Perimeter = f+2s +s+s-5+4`

`Perimeter = f+4s-1`

Substitute values for f and Perimeter

`72 = 4+2s+4s-1`

`72 = 2s+4s-1+4`

`72 = 6s+3`

Collect Like Terms

`6s = 72 -3`

`6s = 69`

`s= 11.5`

`f =4 + 2s`

`f = 4 + 2 *11.5`

`f = 27`

`t = f + s - 5`

`t=27+11.5 - 5`

`t=33.5`

The sides of the triangle are: 11.5, 27 and 33.5