To enclose a field in a shape of right angled triangle, ram used a 30m length wire. the area of the field is 30m2. what is the length largest side of the field
Answers
See the attachment.Explained in well defined manner,hope it helps.
Answer is 13 metre.
Define a, b and c:
Let a and b be the 2 sides of the right angle and c be the hypotenuse.
Using the Pythagoras' Theorem:
a² + b² = c² ---------------------- [ 1 ]
Using the perimeter:
Perimeter = Side 1 + Side 2 + Side 3
a + b + c = 30
a + b = 30 - c ---------------------- [ 2 ]
Using the area:
area = 1/2 base x height
30 = 1/2 ab
ab = 60 ---------------------- [ 3 ]
Putting all the equations together:
a² + b² = c² ---------------------- [ 1 ]
a + b = 30 - c ---------------- [ 2 ]
ab = 60 -------------------------- [ 3 ]
From [ 2 ] :
a + b = 30 - c
(a + b²) = (30 - c)²
a² + b² + 2ab = 30² + c² - 60c -------------------------- [ 4 ]
Substitute [ 1 ] and [ 3] into [ 4 ]:
a² + b² + 2ab = 30² + c² - 60c
(a² + b²) + 2(ab) = 30² + c² - 60c
c² + 2(60) + = 900 + c² - 60c
120 = 900 - 60c
60c = 780
c = 13 m
Answer: The longest side is 13 m