Solve each problem. See Example 1. Michael must build a rectangul...

Question

Solve each problem. See Example 1. Michael must build a rectangular storage shed. He wants the length to be 6 ft greater than the width, and the perimeter will be 44 ft. Find the length and the width of the shed.

Accepted Answer

Welcome back. I am so glad you're here. We have this rectangular shaped swimming pool. Let's make it blue because it's a pool and we are told that the length of the pool this can be the length is, means equals in math language is eight ft greater than so eight ft greater than the width of the pool. So eight plus W is equal to L and here over here is our width, suppose the perimeter of the pool, okay. Perimeter is adding all the sides together. So that's going to be, that could be L plus L because he would be another L plus W plus W there's another W that equals the perimeter or we could rewrite that we can combine like terms L plus L is two, L plus W plus W is two, W That's the perimeter and it's equal for this pool to 60 ft. Alright, so we need to find the length and the width of our pool. Well, we've got L in terms of W here because L equals eight plus W. So we can substitute in for L in our equation over here, we can substitute this eight plus W. So we'll have two times no longer. L but now eight plus W in parentheses, bring down the plus two W and that's equal to 60. It is 60 ft. I'm going to drop the feet just for the sake of fewer letters. While we're looking at this. Now, we can solve for W we can figure out the width so we can distribute that to in front of the eight plus W two times eight is 16 plus two times W is two, W bring down the plus two, W equals 60. We can combine like terms. We have two W plus two, W That equals four, W And we can subtract 16 from both sides in order to bring the constant terms together. On the right hand side, opposite of the WS 60 -16 equals 44. We have almost solved for W we can divide both sides by four. On the left. We just have W now and that equals on the right hand side, 44 divided by four is 11. And we have solved for our width. Now, we just need to solve for our length. We know what W is. So we can substitute that in, for the W, in our length equals eight plus W. So this will be length equals eight plus no longer. W that is 11 Well, eight plus 11 that equals 19 sore length is 19. We look at our answer choices for a length of 19 ft and a width of 11 ft and that matches with answer choice B well done. We'll catch you on the next one.

Solve each problem. See Example 1. Michael must build a rectangular storage shed. He wants the length to be 6 ft greater than the width, and the perimeter will be 44 ft. Find the length and the width of the shed.

Key Concepts

Perimeter of a Rectangle

Algebraic Expressions

Solving Linear Equations

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