s = length of the shortest side of the triangle
m = length of the medium side of the triangle
l = length of the longest side of the triangle
(you can use different variables like l, w, h, x, y.......)
Perimeter(P) of a triangle is the total sum of the sides, in this case:
P = s + m + l
You know:
P = 26in
l = s + 3 [longest side is 3in longer/more than(addition) the shortest side]
m = s + 2 [medium side is 2in longer than the shortest side]
To find the lengths of the three sides, you can do this:
P = s + m + l Substitute/plug in what you know. So plug in 26 into "P" since P = 26, plug in (s + 3) into "l" since l = s + 3, and plug in (s + 2) into "m" since m = s + 2
26 = s + (s + 2) + (s + 3) Combine like terms (like terms have the same variable and power/exponent)
26 = 3s + 5 To find "s", isolate/get the variable "s" by itself. Subtract 5 on both sides
21 = 3s Divide 3 on both sides to get "s" by itself
7 = s
Now that you found s, you can use it to find the other sides
m = s + 2 Substitute/plug in 7 into "s" since s = 7
m = 7 + 2
m = 9
l = s + 3 Plug in 7 into "s"
l = 7 + 3
l = 10
The longest side is 10 inches, the medium side is 9 inches, the shortest side is 7 inches
PROOF
P = s + m + l
P = 7 + 9 + 10
P = 26 inches
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