Question

The first side of a triangle is 3 inches shorter than the second side, and 2 inches longer than the third side. How long is each side, if the triangle has a perimeter of 28 inches?

Answer 1

the length of the first side of the triangle is
`(28)/(3)\ in`

the length of the second side of the triangle is
`(37)/(3)\ in`

the length of the third side of the triangle is
`(19)/(3)\ in`

Explanation:

Let

x-----> the length of the first side of a triangle

y----> the length of the second side of a triangle

z---> the length of the third side of a triangle

we know that

`x=y-3`

`y=x+3` -----> equation A

`x=z+3`

`z=x-3` -----> equation B

The perimeter of the triangle is equal to

`P=x+y+z`

`P=28\ in`

so

`28=x+y+z` -----> equation C

substitute equation A and equation B in equation C

`28=x+(x+3)+(x-3)`

solve for x

`28=3x`

`x=(28)/(3)\ in`

Find the value of each side

the first side of a triangle is x

`x=(28)/(3)\ in`

the second side of a triangle is y

`y=(28)/(3)+3=(37)/(3)\ in`

the third side of a triangle is z

`z=(28)/(3)-3=(19)/(3)\ in`