SOLUTION: a right triangle with an area of 30 square cm has a hypotenuse that is 8 cm longer than the shortest side. Find the dimensions of the triangle

Question 945833: a right triangle with an area of 30 square cm has a hypotenuse that is 8 cm longer than the shortest side. Find the dimensions of the triangle
Found 2 solutions by TimothyLamb, MathTherapy:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
h = s + 8
---
a = bh/2
a = sh/2
30 = s(s + 8)/2
s(s + 8) = 30*2
ss + 8s = 60
ss + 8s - 60 = 0
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the above quadratic equation is in standard form, with a=1, b=8 and c=-60
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 8 -60
into this solver: http://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
---
s = 4.71779789
s = -12.7177979
---
the negative root doesn't fit the problem statement, so use the positive root:
---
s = 4.71779789
h = s + 8
h = 12.71779789
h = sqrt( ss + bb )
hh = ss + bb
bb = hh - ss
b = sqrt( hh - ss )
b = sqrt( 12.71779789*12.71779789 - 4.71779789*4.71779789 )
sqrt( 12.71779789*12.71779789 - 4.71779789*4.71779789 )
---
copy and paste the above expression in to this calculator:
http://sooeet.com/math/scientific-calculator.php
---
b = 11.8103668969
---
answer:
s = 4.71779789 cm
b = 11.8103669 cm
h = 12.7177979 cm
---
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Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

a right triangle with an area of 30 square cm has a hypotenuse that is 8 cm longer than the shortest side. Find the dimensions of the triangle

Altitude (longer leg): cm
Shortest side (shorter leg): cm
Hypotenuse: (longest side): cm
This triangle represents one of the PYTHAGOREAN TRIPLES (5-12-13).

You can do the check!!
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