To do this problem, start with what you know, and write some algebraic expressions for each side.
One side of a triangle is half the longest side.
The third side is 10 feet less than the longest side.
To start, since the first side and the third side are both described in terms of the "longest side", we will assume that the longest side is going to be "x". (which has to be side two)
Now we write the expression "1/2 x" to represent side one.
Then we write the expression "x - 10" to represent side three.
What else do we know? We know that the perimeter is 45 (presumably feet, although you didn't tell us that--we will have to assume that feet are the units here)****.
We also know that the perimeter of a triangle is found by adding the lengths of the three sides together.
Therefore: 45 = side one + side two + side three
Substituting: 45 = 1/2 x + x + (x-10)
Using order of operations, we remove the parenthesis: 45 = 1/2x + x + x -10
Now we combine like terms: on each side of the equation: 45 = 2 1/2x -10
Next we change 2 1/2 to a decimal equivalent so it is easier to work with: 45 = 2.5x -10
Now we isolate x on one side of the equations by adding 10 to both sides: 10 + 45 = 2.5x -10 +10
55 = 2.5x
We continue to work with the coefficient of x to get x by itself. In this case
x is being multiplied by 2.5, so we divide each side of the equation by 2.5: 55 = 2.5x
2.5 2.5
22 = x
Now substitute the number 22 into each of the three expressions you had for the sides:
From above: longest side is going to be "x". (which has to be side two) = 22
Now we write the expression "1/2 x" to represent side one. 1/2 (22) = 11
Then we write the expression "x - 10" to represent side three. 22- 10 = 12
Check to see that it all makes sense: DOES 45 = side one + side two + side three
45 =? 11 feet + 22 feet + 12 feet
Yes! 45 feet = 45 feet
****If the number 45 in the original problem is 45 yards or some other unit, there would need to be a conversion to feet before you did this problem.
