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?

this is confusing. explain step by step

Since  

x

is 8 in. shorter than the second side, we know that we'd need to add 8 to  

x

to get the length of the second side. So the second side is  

x

+

8

. (Think, if the first side is 2 inches and it is 8 inches shorter than the second side, the second side must be 10 inches, so this works.)

The third side is 4 times the length of the first side, so the third side is  

4

x

.

Perimeter is the sum of the sides, so:  

( x ) + ( x + 8 )+ 4 x = 6 x+ 8

We also know the perimeter is 26, so we have:

6 x + 8 =26

subtract 8:

6 x =18

divide:

x = 3 .

The three sides have length: 3, 11, and 12.

The longest side is 12 inches long.

Step-by-step explanation: