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14 December, 00:41

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

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  1. 14 December, 01:07
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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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