The first side of a triangle is 8m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side

Call the length of the second side ' S '.

(It could have any name. I just felt like calling it ' S ' for 'second'.)

The first side is 8m shorter = S - 8.

The third side is 4 times as long as the first side = 4 (S - 8).

When you add up all three sides, you have

(S - 8) + (S) + 4 (S - 8).

That's a mess.

We need to clean it up.

Eliminate the parentheses: S - 8 + S + 4S - 32.

Add up all the S's: 6S - 8 - 32

Add up all the plain numbers: 6S - 40.

That's the sum of all the sides.

Another name for it is 'perimeter'.

The question says it's 26m.

So we can write 6S - 40 = 26

Add 40 to each side: 6S = 66

Divide each side by 6 : S = 11 m

First side = S - 8 = 3 m

Second side = S = 11 m

Third side = 4 (S-8) = 12 m