Question 167676: A RIGHT TRIANGLE HAS A HYPOTENUSE WITH A MEASURE OF 20 CM. FIND THE LENGTHS OF THE LEGS IF ONE LEG IS 4 CM LONGER THAN THE OTHER LEG.
Answer by sowmya(32)   (Show Source):
You can put this solution on YOUR website! A RIGHT TRIANGLE HAS A HYPOTENUSE WITH A MEASURE OF 20 CM. FIND THE LENGTHS OF THE LEGS IF ONE LEG IS 4 CM LONGER THAN THE OTHER LEG.
Solution:
In aright trianle with sides a , b and hypotenuse c units,
by pythagoras theorem
c^2 = a^2 +b^2
Let a = b+4
c = 20 cm (given)
Hecne by the theorem,
400 = (b+4)^2 + b^2
= 2b^2 + 8b + 16
2b^2 + 8b -384=0
=> b^2 +4b - 192 = 0
b^2 + 16b - 12 b -192=0
(b-12)(b+16) = 0
b = 12 or b = -16
but b cannot be neagtive since b is a side lenghth
b = 12,
a= 16
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