SOLUTION: The area of right angle triangle is 30cm2 and the length of its hypotenuse is 13 cm. the length of the shorter leg is:

Algebra ->  Triangles -> SOLUTION: The area of right angle triangle is 30cm2 and the length of its hypotenuse is 13 cm. the length of the shorter leg is:       Log On


   

Question 884695: The area of right angle triangle is 30cm2 and the length of its hypotenuse is 13 cm. the length of the shorter leg is:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29AB=30
AB=60
.
.
A%5E2%2BB%5E2=13%5E2
A%5E2%2BB%5E2=169
From the first equation,
A=60%2FB
Substitute,
%2860%2FB%29%5E2%2BB%5E2=169
3600%2FB%5E2%2BB%5E2=169
3600%2BB%5E4=169B%5E2
B%5E4-169B%5E2%2B3600=0
%28B%5E2-17B%2B60%29%28B%5E2%2B17B%2B60%29=0
%28B-5%29%28B-12%29%28B%2B5%29%28B%2B12%29=0
Only the positive solution works here.
Two solutions:
B-5=0
B=5
Then,
A=60%2F5
A=12
and
B-12=0
B=12
Then,
A=60%2F12
A=5