One of the sides of a parallelogram has the length of 5 in. Can the lengths of the diagonals be:
4 in and 3 in?
Its no i got it correct yay
no
It is no because the triangle can't have sides 1.5, 2, and 5.
The diagonals bisect each other.
That means you will have a triangle with sides 1.5, 2, 5
Is that possible?
To determine if the given lengths can be the diagonals of a parallelogram with one side measuring 5 inches, we can use the Parallelogram Diagonal Theorem. According to this theorem, the sum of the squares of the lengths of the diagonals in a parallelogram is equal to the sum of the squares of the lengths of its sides.
Let's denote the lengths of the diagonals as d1 and d2, and the length of one side as a. Based on the given information:
d1 = 4 in
d2 = 3 in
a = 5 in
We need to check if the Pythagorean theorem holds true for these values. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the theorem, we can check if the length of the diagonals follows this pattern:
d1^2 + d2^2 = a^2
Substituting the given values:
(4^2) + (3^2) = 16 + 9 = 25
Since 25 is equal to 5^2, the equation holds true. Therefore, the given lengths can indeed be the lengths of the diagonals of a parallelogram with one side measuring 5 inches.