Solve each problem. See Example 1. The perimeter of a triangul...

Question

Solve each problem. See Example 1. The perimeter of a triangular plot of land is 2400 ft.The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot.

Accepted Answer

Welcome back. I am so glad you're here. We are told that a farmer is harvesting a crop field which is triangular and shape. Alright, let's draw a triangle here and the perimeter is 3000 ft. What we recall from previous lessons, that perimeter is going to be when you add all the sides together, let's call them A B and C. And so, in other words, if we take A plus B plus C, that equals 3000 ft, the measure of the longest side, let's say that C is the longest side. The measure of that longest side is we recalled, it is means equals so C equals ft less than okay. So we'll be taking something minus 101 100 ft less than thrice the measure of the shortest side, let's say that A is the shortest side and thrice that is going to be three A. So C equals three A minus 100. The measure of the middle sign. So that's going to be, be, Is 300 ft less than Okay. So is equals 300ft less than we're going to be taking away 300. The measure of the longest side. Okay. Well, the measure of the longest side is three a -100. So B is three A -100 -300. Find the measure of all of the length of the field. So we have to find what A B and C are equal to. Well, now we have formulas in terms of A four B and C. So we can substitute those into our A plus B plus C equals 3000 will bring down A, that one's fine. Plus B will be, we will substitute in three A minus 100 minus 300. We can even simplify that before we go in, we can combine the like terms minus 100 minus 300 is minus 400. So this is three A minus 400 in for B. So we have a plus three A minus 400 for R B and then substituting for C, that's going to be the three A minus 100. So plus three A minus still equals 3000. Now, let's combine like terms, we've got a plus three A, that's +48 plus three more eights. That's seven A s so we've got seven A And now we'll combine these constant terms negative 400 -100. That's going to be -500, Still equals 3000. Now, in order to get this a by itself, first, we'll add, oops, I wanted to switch colors first, we will add 500 to both sides. So on the left will have seven a and on the right, that will equal 3000 plus 500 is Is almost by itself, will divide both sides by seven. And we get a equals 3500, divided by seven is 500. A equals 500. We got one of them. Now, we can plug that in to our formulas here to see what B and C equal. So plugging it in Here, we're plugging in 500 for a. That's three times 500 -400. for RB three times 500 is -400 equals 1100. So be measures 1100. These are all feet. Now, let's substitute in for C for C will be substituting again 500 for a. So if three times 500 -103 times 500 is still -11500 -100 equals 1400. So that longest side is 1400 ft. And we have solved for all three sides. So we look at our answer choices for measurements of 500 ft, 1100 ft and 1400 ft. And that matches with answer choice. B well done. We'll catch you on the next one.

Solve each problem. See Example 1. The perimeter of a triangular plot of land is 2400 ft.The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot.

Key Concepts

Setting Up Algebraic Expressions from Word Problems

Forming and Solving Systems of Linear Equations

Understanding Perimeter and Triangle Side Relationships

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