Question 883090

How do you find the 2 other side lengths of a right triangle if you are given a side length and the perimeter of that triangle... for example: the perimeter of a right triangle is 40m, The length of the longest side of the triangle is 17m, what are the lengths of the other two sides?
<pre>
Let length of shorter and longer legs, be S and L, respectively
Then S + L + 17 = 40
S + L = 23____S = 23 – L ---- eq (i)
{{{S^2 + L^2 = 17^2}}} ----------------- eq (ii)
{{{(23 - L)^2 + L^2 = 17^2}}} ---------- Substituting 23 – L for S in eq (ii)
{{{529 - 46L + L^2 + L^2 = 289}}}
{{{L^2 + L^2 - 46L + 529 - 289 = 0}}}
{{{2L^2 - 46L + 240 = 0}}}
{{{2(L^2 - 23L + 120) = 2(0)}}}
{{{L^2 - 23L + 120 = 0}}}
(L - 15)(L - 8) = 0
L, or longer leg = {{{highlight_green(highlight_green(15m))}}}
S = 23 – 15 ------- Substituting 15 for L in eq (i)
S, or shorter leg = {{{highlight_green(highlight_green(8m))}}}
You can do the check!! 

Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
Further help is available, online or in-person, for a fee, obviously. 

For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL MATH QUESTIONS, MATH HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra,
Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,
GRE, CLEP,and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/.