SOLUTION: 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

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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?
Found 2 solutions by JulietG, MathTherapy:
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter is A + B + C. We know that C = 17. Therefore A+B = 40-17, or 23
a%5E2+b%5E2=c%5E2
a%5E2+b%5E2=289
.
If we *assume* that the sides are whole numbers, the possibilities are combinations that equal 23. Let's use estimating - try using 10 (since it's easy). Then we would have
10*10 + 13*13
100 + 169
Too little.
9*9 + 14*14 =
81 + 196
Still too little
8*8 + 15*15
64 + 225
Success!

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

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?


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%5E2+%2B+L%5E2+=+17%5E2 ----------------- eq (ii)

%2823+-+L%29%5E2+%2B+L%5E2+=+17%5E2 ---------- Substituting 23 – L for S in eq (ii)

529+-+46L+%2B+L%5E2+%2B+L%5E2+=+289

L%5E2+%2B+L%5E2+-+46L+%2B+529+-+289+=+0

2L%5E2+-+46L+%2B+240+=+0

2%28L%5E2+-+23L+%2B+120%29+=+2%280%29

L%5E2+-+23L+%2B+120+=+0

(L - 15)(L - 8) = 0

L, or longer leg = highlight_green%28highlight_green%2815m%29%29

S = 23 – 15 ------- Substituting 15 for L in eq (i)

S, or shorter leg = highlight_green%28highlight_green%288m%29%29

You can do the check!! 



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