A rectangular soccer field is twice as long as it is wide. If ...

Question

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

Accepted Answer

Hello. Today we're going to be solving for the length and width of a rectangle. So the word problem states that a garden which is rectangular length is the rice as long as its width. What are the length and width of the garden if its perimeter is 80 yards? So let's go ahead and note a couple of things from the word problem. We are told that the garden has a rectangular shape so we can go ahead and draw a rectangle to represent this garden. Now we are told that the length is thrice as long as the width. Well what thrice means is three times and we don't know what the length or width is but we can represent those unknown values with the variable X. So width is going to be X. But length is going to be three X. Because it's three times as long as the width. Now how can we solve for X. While we are told That the perimeter is 80 yards and the perimeter of a rectangle is to length plus two width. While again perimeter is 80 yards. So we can represent P with 80 and length is three X. So this is going to be two times three X. And that's going to be plus two times with which is just X. So what we need to do is go ahead and simplify this equation here in order to be able to solve for a missing length and width. So 80 is equal to two times three X plus two X. Multiplying two and three X together is going to give us six X. So we have 80 is equal to six X plus two X. Six X plus two X is going to give us eight X. So 80 is equal to eight X. And in order to solve for X here we can divide both sides of this equation by eight and X is going to equal to 10. So we have a value for X which is 10. So we can go ahead and represent the width As yards. Now we know what the width is, but we still need to solve for length because length is three times as long as the width while we just go ahead and take our value of X and plug it in for the length. So length is going to equal to three times 10, which is equal to 30 yards. So that means the dimensions of this rectangle represented by length by width is going to be 30 yards by 10 yards. And that's gonna be the dimensions of this rectangular garden. And that also means that the answer to this problem is going to be deep. So, I hope this video helps you in understanding how to solve this type of word problem. And I'll go ahead and see you all in the next video

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

Key Concepts

Perimeter of a Rectangle

Algebraic Representation of Relationships

Solving Linear Equations

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