the perimeter of a triangle is 31 cm. sides #1 and #2 have epual length, while side #3 is one centimeter shorter than twice the length of side #1. how long is each side
2x + (2x - 1) = 31
4x - 1 = 31
4x = 32
x = 8
The sides must be 8, 8, and 15
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To find the lengths of each side of the triangle, let's assign variables to the unknown lengths.
Let's call the length of side #1 as x, and since side #2 has equal length, it is also x. Side #3 is one centimeter shorter than twice the length of side #1, so it can be expressed as (2x - 1).
Now, we know that the perimeter of a triangle is the sum of the lengths of its sides. Therefore, we can write the equation:
Perimeter = Side #1 + Side #2 + Side #3
Substituting the assigned variables, we have:
31 = x + x + (2x - 1)
Simplifying the equation, we combine like terms:
31 = 4x - 1
Next, we isolate the variable by bringing -1 to the right side:
31 + 1 = 4x
32 = 4x
Now, divide both sides by 4 to solve for x:
32/4 = x
x = 8
So, each side has a length of 8 cm.