Question 142479
Perimeter equals P
P=378
The problem describes two sides of the triangle.The shortest side is 30 yards longer than one-half of the longest side. The second longest side is 2 yards shorter than the longest side. It doesnt however describe the last side. We do not know anything about the side so we will refer to it as x. So our longest side equals x and we will refer to every other side in relation to x.
The Longest side =x
The Shortest side=1/2x +30
The Middle side=x-2

To find the perimter of a figure you must add all of the sides together. Because we are dealing with letters and numbers instead of just numbers it will be slightly more algebraic but we can do it. So we know the what the sides are equal to, so lets solve for x. We know that the perimeter equals 378, so lets add our sides together. We have x+(1/2x+30)+x-2=378. At this point we need to add together our common terms on the left side. So we will add our x's and then our numbers. So we then have 2 1/2x+28=378. Now we need to begin solving for x. We need to begin but getting the x and the number in front of it by itself. Because 28 is a positive number we need to subtract 28 from both sides to get the x and its coefficient by itself. This gives us 2 1/2x+28-28=378-28. We do the math and we have 2 1/2x=350. Now we need to get the x by itself. Again we must do the opposite function, which is divide in this case because the 2 1/2 is being multiplied by the x. So we have x=350 divided by 2 1/2. We do the math and we know that x=140. Now we have solved for x but we have not finished the problem. We now only know what the longest side is equal to. We need to go back and plug x in to our equations for the middle and shortest side and check our work.
Middle side:140-2=138
Shortest side:1/2(140)+30
              70+30=100
Now we have to add together our three sides to be sure that they equal the correct perimeter. 100+138+140=378. Our answer checks out, its always good to check our work.