The length of the rectangular tennis court at Wimbledon is 6 f...

Question

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

Accepted Answer

Welcome back. I'm so glad you're here. We've got this auditorium and it's in new york city which I guess I mean it has so many auditoriums that now they're using it for conferences instead of concerts or something like that. So this auditorium for conferences is rectangular in shape. So we know it's got a length and a width and we are told that the length is 25 ft longer than thrice the width. How could we rewrite that? Okay thrice the width means three times the width or three W. And 25 ft longer. That means we're going to add 25 ft to that. So L the length is three W plus 25. What else do we know about this auditorium used for conferences? Well we know that the perimeter of the auditorium is 650 ft. So we can say p equals and were asked to find the dimensions. Well the dimensions, that's the length and the width or the width and the length. So what else do we know? Well we also know another formula for a perimeter of a rectangle. We know that the perimeter is all the sides added up together. This would be another W. This would be another L. So we could rewrite that as instead of W plus W plus L plus L. It's two W Plus two L. Well now we've got three different formulas and we can use some substitution into this formula here so that we can solve for our dimensions over here, We know that P is 6:50. So we can replace this P with 650. We have two W plus two and we know that L. Well that is three W plus 25. So we can replace our L. With three W plus 25. And now the only variable we've got is W. And we can just solve for w solve for our width. Let's distribute that too. So we've got 650 equals two. W plus two times three. W is six, W plus two times 25 is 50. Now we're going to combine our W terms are like terms and let's bring that 50 over to the left hand side where there are no W. S. So we subtract 50 from both sides. 6 50 minus 50 is 600 equals two. W plus six. W. Is eight W. Now let's get that w by itself and we'll divide both sides by eight. 600 divided by eight is 75. So our W equals 75. Yeah, we got one of our dimensions and now we can plug this W equals 75 in for our W. Here. To solve for L. Because L equals three W plus 25. So now we can write three times 75 plus 25 3 times 75 is 225 plus 25 to 25 plus 25 is 2 50. R. L equals to 50. And we can write that up here. So we have 75 ft by 250 ft. Because recall that our dimensions are in feet, we look at our answer choices and this matches with answer choice. C. Well done, we'll catch you on the next one.

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

Key Concepts

Formulating Algebraic Expressions from Word Problems

Perimeter of a Rectangle

Solving Linear Equations

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