the are of a rectangular

Question

the area of a rectangular wall of a barn is 28 sq ft. its length is 12 ft longer than the width. find the length and width of the wall of the barn

Answer 1

One of the easiest ways to solve a word problem is to break the information contained in it up into separate sections. With that in mind let's look at the problem and see what relevant information we find.

 

The first sentence reads "The area of a rectangular wall of a barn is 28 sqft." This is a pretty straight forward sentence that we will use in the rest of the problem as a base number for further calculation. The important points of this section are that the wall is rectangular and that its area is 28 sqft.

 

The second part of the sentence reads "Its length is 12 ft longer than the width." So we know that because it is a rectangle the sides will not be exactly the same length. This section of the sentence shows us that the length is 12 feet longer than the width.

 

Now that we have broken the problem into the important parts, we need to find the length and width of the wall of the barn. To summarize, we already know that the area is 28 square feet and that one side of the wall is 12 feet longer than the width.

 

height = ?

length = height + 12 feet

area = 28 sqft

 

The next step of this problem would be to take the information and break it up into a mathematical expression.

 

We can describe the given information we found by substituting the unknown elements for a variable. So with that in mind we will substitute the height for the variable "X".

 

height = x feet

length = x + 12 feet

area = 28 square feet

 

Now we need to think about how to get the unknown side of the rectangle of the barn (x) from the known area of the rectangle. Well, if we consider the formula for calculating area we may just find a solution that benefits us.

 

Area Formula:

The area of a rectangle is given by multiplying the width times the height.

 

If we were to express this as a mathematical function with the information from the problem we could say that "x" (our height) multiplied by x +12 (our length) = 28 square feet (our area).

 

x * (x+12) = 28

 

With what we know of the problem we can now start to solve for x to get the measurements of the sides.

 

To solve this problem we first should reorder the terms:

x(12+x) = 28 which if we break it down further is the same as saying (12 *x + x * x) = 28 if we simplify the expression further for this new equation of (12 * x + x * x) = 28 we get (12x + x²) = 28.

 

With this simple expression we no longer need the parenthesis so we have 12x + x² = 28 and can now start solving for "x" in the problem.

 

Now the problem is simple enough to ask ourselves it's solution. What number multiplied by 12 added to the square of that number is equal to 28. If we continue to break the problem down we see that the answer is two.

 

We can prove our result by plugging it in to the original equation and checking it equates correctly. If we plug 2 into the original problem we get 2*(2+12) = 28 which we can see is a truthful statement.

 

Taking this information back to the word problem we can say that we have solved for x (our height) so our calculations become:

height = 2 feet

length = 2 + 12 feet = 14 feet

area = 28 square feet

 

I truly hope that helps. Please let me know if you have any other questions or feel free to schedule a tutoring session if you would like one on one help!