Solve each problem. See Example 1. The length of a rectangular la...

Question

Solve each problem. See Example 1. The length of a rectangular label is 2.5 cm less than twice the width. The perimeter is 40.6 cm. Find the width. (Side lengths in the figure are in centimeters.)

Accepted Answer

Welcome back. I am so glad you're here. We are told about this garden. Let's draw a nice rectangular garden and we're told that the length. All right here, it will be the length of the garden is, is, is equals and math language 6.8 ft less than so we're going to be subtracting 6.8 from something less than thrice the width. Alright. Well, that's three times the width. The width is over here of the garden. Suppose that the perimeter of the garden. Okay. Well, we know that the perimeter is adding all of the sides together. So that's length plus length. This would be another length plus width plus width because this would be another width equals the perimeter or we can combine those L's together. They're like terms that would be to L and combine those W together. That would be plus two. W there's our perimeter. The perimeter of the garden is 80.8 ft. So two L plus two, W equals 80.8, find the length and the width of the garden. So we're solving for L and W. All right. Well, we have got L in terms of W here. So we can substitute for L in our equation two L plus two, W equals 80.8. And we can put in that three, W minus 6.8 for L. So this would be two times Not L but three W -6.8 and still plus two, W equals 80.8. Now, we can solve for the width distributing that to in front of the three W minus 6.82 times three, W equals six W and two times negative 6.8, that equals negative 13. still plus two, W equal to 80.8. Now, we want to do a couple things. We want to bring the constant terms together on the right hand side of the equation. So we can add 13.6 to both sides. And we want to combine like terms this six W and the two W. So six W plus two, W equals eight W And on the right hand side, 80.8 plus 13.6 equals 94.4. We almost have this soft, we want to divide both sides by eight to find W we divide both sides by eight and we have W equals 94.4, divided by eight is 11.8. So we found our width, it's 11.8. Now we just have to figure out the length and we'll just substitute in for our W here in the length. Equals three, W minus 6.8 will substitute 11.8. So we have the length equals three times no longer. W but now 11.8 And then that is -6.8, still three times, 11.8 equals 35.4. Still -6.8 and 35.4 minus 6.8 equals 28.6. So our length is 28.6. We have solved for our length and our width, we look at our answer choices for a length of 28.6 ft and a width of 11.8 ft. And that matches with answer choice d well done. We'll catch you on the next one.

Solve each problem. See Example 1. The length of a rectangular label is 2.5 cm less than twice the width. The perimeter is 40.6 cm. Find the width. (Side lengths in the figure are in centimeters.)

Key Concepts

Perimeter of a Rectangle

Algebraic Expressions

Solving Linear Equations

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