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The area of a rectangle is 27 sq ft. The base is 3 more than twice the height. Find the dimensions of the rectangle. whats the perimeter?

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3 Answers

Always remember to start by writing down what you know for sure from what they tell you in the problem. The first piece of information is that the figure is a rectangle, and the second is that they are giving you the area. So, start with the formula for the area of a rectangle, Area= (B) * (H). Now put in the rest of the information they've given you. This Area is equal to 27 square ft. So substitute 27 for A in the equation above.  27 = B*H. 

Now, as Sheila recommended, describe the relationship between the base and height in numbers: 

B=2H +3 ("The base is equal to 3 more than (use addition) twice (multiply it by two) the height."

Now you have quantities that describe the relationship between base and height (the Area) and a quantity for one in terms of the other. Can you put these together? Sure you can! Put the description for B in the Area formula. 

27 = H(2H +3) ... If you distribute the H through the parentheses and bring the 27 over to the right hand side of the equation..... you'll be headed toward a trinomial that needs factoring. You'll actually get two answers, but one of them doesn't fit the requirements of the question, so you can throw it out.... Always remember to check your answer to see if it fits. 

Now that you have dimensions that fit the area requirement, you can label your rectangle and add up the side lengths to get the perimeter. 

Good luck.

Mental math appoach:

B = base

H = height

Since the area = 27 = B*H, factor 27 into B and H such that  B is 3 more than twice the H.

27 = 9*3 gives the result: B = 9, and H = 3.

The perimeter = 2(B+H) = 2(9+3) = 24 <==Answer

 

 

Hi, Rosa.

The word "dimensions" is talking about the base and height of the rectangle.  This problem is asking you to find the base, height, and perimeter of the rectangle described.

If you are looking for help in setting up this problem, think about a way to represent the length and width using variables.  "The base is 3 more than twice the height."  Suppose you let the letter h represent the height.  Twice the height would be 2h.  And three more than twice the height would be 2h + 3.

Height = h
Base = 2h + 3

Recalling how to find area of a rectangle, you will need to multiply the base times the height (or length times width).  So that would look something like this:
A = h (2h + 3)  
27 = h (2h + 3)

Do you know how to solve it from here?