Question 1085090
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Let x be the shorter leg of the triangle, in centimeters.


Then the length of the longer leg is (x+3) cm, according to the condition.


The Pythagorean theorem says

{{{x^2 + (x+3)^2}}} = {{{15^2}}},   or

{{{x^2 + x^2 + 6x + 9}}} = 225,

{{{2x^2 + 6x - 216}}} = 0,

{{{x^2 + 3x - 108}}} = 0.


Factor left side:

(x-9)*(x+12) = 0.


The roots are x= 9 and x= -12.


Ignore the negative root, since the length can not be negative.


The only solution to the problem is x= 9 cm.


<U>Answer</U>.  The legs of the given right-angled triangle are 9 cm and 12 cm.

         It is the classic (3-4-5)-right-angled triangle.
</pre>


To see more similar solved problems, look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-the-perimeter-of-a-triangle.lesson>Solved problems on the perimeter and side lengths of a triangle</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-the-perimeter-and-side-lengths-of-a-right-angled-triangle.lesson>Solved problems on the perimeter and side lengths of a right-angled triangle</A>

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
"<U>Finding the perimeter and sides lengths of triangles, parallelograms, rectangles and polygons</U>".