Question

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

Answer 1

See the attachment.Explained in well defined manner,hope it helps.

Answer is 13 metre.

Answer 2

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