The longest side of a triangle is 3 in. longer than the shortest side. The medium side is 2 in. longer than the shortest side. If the perimeter of the triangle is 26 in., what are the lengths of the three sides?

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

shortest side = 7 in

Medium side = 9 in

The longer side = 10 in

Step-by-step explanation:

Let x represent the smallest side of the triangle.

The longest side of a triangle is 3 in. longer than the shortest side. It means that the length of the longest side is x + 3

The medium side is 2 in. longer than the shortest side. It means that the length of the medium side is x + 2. If the perimeter of the triangle is 26 in, it means that

x + x + 2 + x + 3 = 26

3x + 5 = 26

3x = 26 - 5 = 21

x = 21/3 = 7

The medium side is x + 2 = 7 + 2 = 9 in

The longer side is x + 3 = 7 + 3 = 10 in

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .