Peter J.

asked • 05/31/15

I still cant do these problems

The length of the longer leg of a right triangle is


25m
more than seven times the length of the shorter leg. The length of the hypotenuse is


26m
more than seven times the length of the shorter leg. Find the side lengths of the triangle.
 

Length of the shorter leg:





m


Length of the longer leg:





m


Length of the hypotenuse:

2 Answers By Expert Tutors

By:

Michael J. answered • 05/31/15

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Applying SImple Math to Everyday Life Activities

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Assign variables for the dimensions we want to find.  Since everything is being compared to the shorter leg
 
Let shorter leg = x
Let longer leg = 7x + 25
Let hypotenuse = 7x + 26
 
Since we have the right triangle, we use the Pythagorean theorem.
 
x2 + (7x + 25)2 = (7x + 26)2
 
 
Expand this out.
 
x2 + 49x2 + 350x + 625 = 49x2 + 364x + 676
 
50x2 + 350x + 625 = 49x2 + 364x + 676
 
 
Make the right side of equation equal zero by bringing all terms to the left side.
 
x2 - 14x - 51 = 0
 
 
Factor the left side of equation.
 
(x - 17)(x + 3) = 0
 
x = 17    and    x = -3
 
 
Now we validate these values of x.  Since we cannot have a negative value for dimensions, we accept the solution
 
x = 17
 
 
Substitute this value of x into the dimensions.
 
shorter leg = 17 m
longer leg = 144 m
hypotenuse = 145 m
 
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Peter J.

THANK YOU. I saw what you doing but I still cant do it. I am trying to do another one it seems confused me
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05/31/15

Michael J.

Which part in these types of problems troubles you the most? I can explain further to you from there.
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05/31/15

Peter J.

I don't know how to start it
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05/31/15

Michael J.

In the problem, you are given information that can be used in the process, such as numbers.  But before that, you must understand the concept behind the problem and what it is asking.  For example, the problem uses the terms "right triangle" and "hypotenuse".  These two terms should ring something in your mind: Pythagorean theorem.  Getting back to the given information, it gives you numbers to use and words that can be translated into algebraic expressions.  Combine those numbers and words to establish variables that represents the problem.  In this problem, it asks us to find the 3 legs of the triangle.  They give us the legs, but in terms of words and numbers we can use to write those variables.  Lets take the length of the longer leg is 25 more than 7 times the shorter leg.  We do not know the actual length of these legs as of now, but according to the information given, we can use them to write variables and expressions to represent them. Therefore,
 
We let the shorter leg = x  ,
since this leg seems to be the most simple quantity.
 
We also know the length of the longer leg in terms of algebraic expressions.
 
Longer leg = 7x + 25
 
This expression resulted from translating the words from the problem that represented the longer leg. 
We also do the same to the hypotenuse.  The longer leg and hypotenuse are the same lengths, but one more than the hypotenuse is 1 more than the longer.  This is because they have a 7x in common.
 
Hypotenuse = 7x + 26        is the result of this part.
 
Now once we have our variables, we use them to write an equation.  Recall the Pythagorean theorem.  We incorporate variables into the theorem and gives us the equation to solve for the variable.  As a result, we obtained
 
x2 + (7x + 25)2 = (7x + 26)2
 
You get it now.
 
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05/31/15

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