Solve each problem. See Examples 1. Dimensions of a Parking Lot. ...

Question

Solve each problem. See Examples 1. Dimensions of a Parking Lot. A parking lot has a rectangular area of 40,000 yd2. The length is 200 yd more than twice the width. Find the dimensions of the lot.

Accepted Answer

Hello, everyone. In this video, we're going to be looking at this practice problem where we want to figure out a gardens length and with and were given a couple characteristics of the gardens lengthen. With first, we know that it's a rectangular garden And its design so that the length is 20 cm more than rice it's with. And the area covered by the garden is 1,024, cm two. So when we think of a rectangle has a width and a length, we know that the area is equal to the width times the length. So in this case, were given that the length Which I'll just write as L is equal to more than Thrice, which is three times the width of three W which means that we can write area in terms of width. So in this case, area would be W times L which is equal to 20 plus three W. And with this, we know that area is 124,000. So I can plug that in here. And now you can see that I have only W that I need to solve for. So I can sell for W first, I'll start by distributing the W. So I have 20 W plus W times three W is three, W squared is equal to 1000. And I'll subtract 124,000 to move all the numbers to one side. And I'll move the three W squared in front Plus 20 w - 1000 is equal to zero. And now you can see that this equation follows the quadratic equation format where we have A X squared plus BX plus C is equal to zero. So that means that we can use the quadratic formula to solve this equation. And recall the quadratic formula is equal to negative B plus or minus the square root of B squared minus four A C divided by two A. So for our equation, You can see that a is the coefficient in front of the variable squared, which is three B is the coefficient in front of the variable by itself, which in this case would be 20. And then finally, C is the constant Or the number at the end of the equation, which in this case is negative 124,000. And if I plug those into the quadratic equation, I get that W is equal to negative 20 plus or minus the square root of 20 squared minus four times three times negative 1000 Divided by two A which is two times 3. And as I start to simplify this, I get W is equal to negative 20 plus or minus 20 squared, which is equal to -4 times three, which is 12 and 12 times 124,000 is equal to one or eight, eight 000 or one million 488, 1,488, Divided by two times 3, which is six. And if we do, Oh, in this case, we have, this is positive because we have the -4 and the negative 124,000 being multiplied together, we get back a positive. So this actually becomes negative 20 plus or minus the square root of 1,488, with 400 divided by six. And now you can see that W could be two values because of the plus or minus. And we can actually simplify the square root of this number because the square root of 1,488,000 with 400 is actually 220. And now we can separate it with the two values because we could have a plus or a minus. So W could be equal to negative 20 plus 1220 divided by six. Or it could be equal to negative 20 minus 1220 divided by six. So if I solve this first one, Negative 20 plus 1220 is 1200 divided by six. So that means the width is equal to 200. And in this case, negative 20-1220 is negative 1240 divided by six. And we can simplify this fraction to negative 20/3. But remember that we're talking about with so a negative with doesn't make a lot of sense. So we can say that the with is equal to 200. And now we know that the length is equal to 20-plus 3 times the width. So I can say link is equal to 20-plus 3 times the width. So the length is 20 plus three times 200. So that's 20-plus 3 times 200 is 600. So that means that the link is equal to 6 20. And we can also check this since we know that the area of the garden should be 124,000. If we do 200, the width times the length of 620, we got 1000. So we know that our within our length are good. So this becomes my final answer for this problem. And if we look at the answer choices, you can see the answer choice B Also has the length at 600 20 cm and the width at 200 cm. So hopefully, this video helped and see you next time.

Solve each problem. See Examples 1. Dimensions of a Parking Lot. A parking lot has a rectangular area of 40,000 yd2. The length is 200 yd more than twice the width. Find the dimensions of the lot.

Key Concepts

Rectangular Area

Algebraic Expressions

Systems of Equations

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