SOLUTION: the area of a right angle triangle is 30 sq. cm and the length of the hypotenuse is 13 sq. cm. the length of the shorter side is?

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Question 351080: the area of a right angle triangle is 30 sq. cm and the length of the hypotenuse is 13 sq. cm. the length of the shorter side is?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
From the Pythagorean theorem,
A%5E2%2BB%5E2=13%5E2
From the area,
%281%2F2%29AB=30
%281%2F4%29A%5E2B%5E2=900
A%5E2=3600%2FB%5E2
Substitute,
3600%2FB%5E2%2BB%5E2=169
3600%2BB%5E4=169B%5E2
B%5E4-169B%5E2%2B3600=0
%28B%5E2-144%29%28B%5E2-25%29=0
Two solutions:
B%5E2=144
A%5E2=25
B=12
A=5
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.
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B%5E2=25
A%5E2=144
B=5
A=12
The shorter leg is 5 cm.