if the perimeter of a parallelogram is 132cm the longest possible length of a diagonal is less then ?
32
To find the longest possible length of a diagonal in a parallelogram, we need to know the dimensions of the parallelogram. The perimeter alone is not sufficient. However, we can still provide some general information.
In a parallelogram, the opposite sides are equal in length, and the opposite angles are equal. Let's represent the length of one side as 'a' and the length of the other side as 'b'. The perimeter of a parallelogram is given by:
Perimeter = 2a + 2b
From the given information, we know that the perimeter is 132 cm. So we can write the equation as:
132 = 2a + 2b
Dividing both sides of the equation by 2, we get:
66 = a + b
Since the longest possible length of a diagonal occurs when the parallelogram is a rectangle (opposite sides are equal and all angles are right angles), we can assume that 'a' and 'b' are equal.
So, substituting 'a' for 'b' in the equation, we get:
66 = a + a
66 = 2a
Dividing both sides of the equation by 2, we find:
a = 33
Therefore, the length of each side of the parallelogram is 33 cm. Since the longest possible diagonal occurs when the parallelogram is a rectangle, in this case, we can use the Pythagorean theorem to find the length of the longest diagonal.
In a rectangle, the length of the diagonal (d) can be calculated using the formula:
d = √(a^2 + b^2)
Substituting the values of 'a' and 'b' (both sides are 33 cm) into the equation, we get:
d = √(33^2 + 33^2)
d = √(1089 + 1089)
d = √2178
d ≈ 46.66 cm
Therefore, the longest possible length of a diagonal is less than approximately 46.66 cm.