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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

User Mohebifar
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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

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