Solve each problem. Dimensions of a Square. If the length of e...

Question

Solve each problem. Dimensions of a Square. If the length of each side of a square is decreased by 4 in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimensions of the original square?

Accepted Answer

Hello, today we're going to be solving the following word problem. So we are told that the length of each side of an equilateral triangle was decreased by two inches. We want to determine the length of each side of the original equilateral triangle. If the perimeter of the new equilateral triangle is 12 inches, more than one third of the perimeter of the original triangle. So in order to solve this problem, let's go ahead and draw a picture. So we know that we want to find the lengths of the original equilateral triangle. And what that means is we have this triangle and because it's equal lateral, each of the sides are going to be of the same length. And since we don't know the length of this triangle or at least the length of each side, we're going to represent one side is X. And since all the sides are equal, each side gets represented by the same variable and the perimeter of this triangle, which I'm going to label S P sub one is just going to be the sum of all the sides of the triangle, which is going to be X plus X plus X. Now simplifying this perimeter X plus X plus X is going to be represented as three X. Now, we are told that we have this new equilateral triangle and this equilateral triangle has all of its sides reduced by two inches. And what that means is each side is going to be two inches less than the original. So we can represent one side as X minus two. Now, since one side of this equilateral triangles, X -2, all the other sides are going to represent to be represented as X -2. And the perimeter of this new triangle, which I'm going to label as P sub two is going to be equal to X minus two plus X minus two plus X minus two. And we can simplify this to be three times the quantity X -2. Now, in order to simplify this perimeter, we can go ahead and distribute three into the quantity X -2 and the second perimeter or at least the perimeter of the new triangle is going to be three X -6. So this is going to be the perimeter of the original triangle and this is the perimeter of the new triangle. And what we are told is that the perimeter of the new triangle is 12" more than 1/3 of the perimeter of the original triangle. So what this means is the second perimeter, which is P two is going to be equal to 12 more, which is 12 plus one third of the original perimeter, which is going to be one third times the first perimeter, which is P one. Now, we can go ahead and substitute P2 MP one with the perimeters we came up with earlier in order to solve for X. So substituting MP two is going to give us three X minus six and that is going to equal to 12 plus 1/3 times the first perimeter, which is going to be three X. And now we want to go ahead and sulfur X on the right hand side, one third times three X is going to simplify to just give us X. So what we have is three X minus six equal to 12 plus X. And since we want to solve for X, we want to go ahead and set this equation equal to zero. So what I'm going to do is I'm going to subtract 12 to both sides of the equation. And I'm going to subtract X to both sides of the equation. That's going to give me two X -18 is equal to zero. Now, What I'm going to do is add 18 to the right hand side of the equation. And that's going to give me two x is equal to 18. And finally, in order to sell for X, I'm going to divide both sides of the equation by two. And that means that X is going to equal to nine. So what that means is the length of each side of the original equilateral triangle is going to be 9". And with that being said, the answer to this problem is going to be c so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Solve each problem. Dimensions of a Square. If the length of each side of a square is decreased by 4 in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimensions of the original square?

Key Concepts

Perimeter of a Square

Algebraic Expressions and Equations

Solving Linear Equations

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