The perimeter of a table tennis top is 28 feet. The difference be...

Question

The perimeter of a table tennis top is 28 feet. The difference between 4 times the length and 3 times the width is 21 feet. Find the dimensions.

A decorative green frame with the word 'LAWN' in red text at the center.

Accepted Answer

Hey everyone in this problem, we're told that the difference between twice the length and four times the width of the lawn is 22 m. Okay. The perimeter is 52 m. And were asked to find the length and width of the lawn, we can see in the diagram here the lawn we're given is a rectangle. So let's start with the first information we're given. We're given the difference between twice the length and four times the width. Okay, so twice a length b. two l. And the difference between four times the width. W. Okay is equal to 22 m. So it gives us this equation here have an equation with two variables L. And W. What about the other piece of information? When we're told the Perimeter is 52 m. We have a rectangle. So the perimeter is going to be two times the length. L Plus two times the width w. And this is going to be equal to 52 m. Alright, so now we have two equations and two unknowns. This is a system. Two equations there. A linear so we can solve them in whatever method we'd like. Let's go ahead and use the elimination or addition method. But you could use substitution if you wanted as well let's label these as equation one and equation to so that we can refer to them later. What we're gonna do is we're gonna take equation one and subtract equation too. Now why do we do that? Okay, what we notice is that equation one and equation to both have to l. Okay if we subtract them to l minus two L. Is going to give us zero, we're going to be left with an equation just with W. Which will allow us to solve for the width W. And then we can come back and solve for the length afterwards. So if we take equation one minus two we have to l minus for W equals 22 m and then we have two L plus two W equals m and we subtract the two To L -2. Well that's going to give us zero and that's why we chose to subtract these equations so we could get that zero there eliminate the variable l. So we can solve for w -4 -2. W. is gonna give us -6 W. On the right hand side, 22 m -52 m. gives us negative 30 m. Now we can solve for w dividing by negative six. We get W. Is equal to five m. Okay? And so the width of the lawn is going to be five m. Now I just need to find the length, we know w we're gonna go ahead and substitute it back into one of our equations. Okay? We can choose to substitute it back into equation one or equation to to find the corresponding length. Okay um The width and the length have to satisfy both of them. So it doesn't matter which one we choose. Um Let's go ahead and just choose one. It was a little bit more room to work. So we're gonna substitute W. equals five m into equation one. This is gonna give us to l minus four times W, which is five m is equal to 22 m To L -20 m is equal to m. Okay, moving the 20 m to the right hand side, we get to L. Is equal to 42 m and dividing by two. The length L. Is equal to 21 m. So we found the width and the length the width is five m. The length is 21 m. So we're gonna have answer d. Thanks everyone for watching. I hope this video helped see you in the next one.

The perimeter of a table tennis top is 28 feet. The difference between 4 times the length and 3 times the width is 21 feet. Find the dimensions.

Key Concepts

Perimeter of a Rectangle

Algebraic Expressions

Systems of Equations

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