a) The hypotenuse of a right angled triangle is 15cm. Taking the perpendicular sides as x, y write the relation connecting the sides B) If the area is 30 centimetre square . Fond the length of its perpendicular sides?
Answers
Given : The hypotenuse of a right angled triangle is 15cm.
perpendicular sides as x, y
To Find : write the relation connecting the sides
B) If the area is 30 centimetre square . Fond the length of its perpendicular sides?
Solution :
Applying Pythagoras theorem
x² + y² = 15²
area is 30 centimetre square
=> (1/2) xy = 30
=> xy = 60
=> y = 60/x
x² + y² = 15²
=> x² + (60/x)² = 15²
Add and subtract 120
=> x² + (60/x)² + 120 - 120 = 15²
=> (x + 60/x)² -120 = 225
or (x - 60/x)² + 120 = 225
=> (x + 60/x)² = 345
(x - 60/x)² = 105
=> Adding both 2x = √345 + √105
=> x = (√345 + √105)/2
x =14.41
6 = 60/x = 4.16
length of its perpendicular sides 14.41 cm and 4.16 cm
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