In Exercises 36–43, use the five-step strategy for solving word p...

Question

In Exercises 36–43, use the five-step strategy for solving word problems. The length of a rectangular field is 6 yards less than triple the width. If the perimeter of the field is 340 yards, what are its dimensions?

Accepted Answer

Welcome back. I'm so glad you're here. We are going to find out the length and the width of this lovely rectangular auditorium that I'm drawing. So we've got the length is L. And we can choose any letters for these. But just quickly looking at the answer choices, they've got an L. And they've got to be so for the width we'll choose B. And um we know it's the same on both sides because it's a rectangle. What else do we know about this auditorium? Well we can write a couple of math sentences about it. We know that the width. So that's our B. Is that means equals to units less than Okay, two units less than is A minus two. It's a little too less than something that goes before it, what goes before it half of its length. So we can write that as one half L. So that's our first math sentence B equals one half L minus two. That's for the width. Now we can write that second sentence. The perimeter. Okay, perimeter. We find that by saying, okay, all the sides added together. So that would be L plus L plus B plus B. Or we can simplify that to two L. Plus to be that's our perimeter to L plus two B. And we know that that is or equals units. So that's our second sentence and now we can combine them to isolate the B and L. To solve for them and find their length and their width. And because we have that be by itself, we are going to use substitution. So when there's a bee down here we can substitute for what the B. Is equivalent to which is one half l minus two. Now I'll rewrite two L. Plus instead of to be it's two parentheses one half l minus two equals 32 still. And we can distribute that too. So we'll bring down the two hour plus. Now it's two times one half. That's just one. So times L. And two times negative two is negative four equals 32 combining like terms to L. Plus L. Is three. L minus four equals 32 will add affordable sides. So we've got three L equals 36 divide both sides by three and we've got L equals 12. And hey look at that. We have solved for the length. Now we've just gotta solve for R width in order to do that. We're going to plug L into, we could do either sentence but it's easier to do the first one this time because the B. The width that we're looking for is already isolated. So we'll only have to deal with the right hand side of the equation so we can rewrite that B equals one half not L. But now 12, 1 half times 12 minus two. We know that one half times 12 is six, B equals six minus two, simplifying that B equals four. And we have solved for our length and our width. We look carefully at our answer choices and that matches answer choice A well done, we'll catch you on the next one.

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