The length of diagonals of parallelogram is 8 cm and 6 cm respectively and the measure of one of its side is 5 cm. Find the approximate length of other side (in cm).

Correct option is B

Concept/Formula Used:

In a parallelogram, the diagonals bisect each other. Using the diagonal lengths, we can calculate the sides using the diagonal formula:

$$a^2 + b^2 = \frac{d_1^2 + d_2^2}{2}$$​​

where:
- a : the length of one side,
- b : the length of the adjacent side,
- $$d_1, d_2$$​ : the lengths of the diagonals.

Step 1: Given Values:

- $$d_1$$​ = 8 cm (length of one diagonal)
- $$d_2$$​ = 6 cm (length of the other diagonal)
- a = 5 cm (length of one side)

Step 2: Use the Parallelogram Diagonal Formula:

The relationship between the diagonals and sides is given by:

$$a^2 + b^2 = \frac{d_1^2 + d_2^2}{2}$$​​

Substitute $$d_1 = 8 , d_2 = 6$$​:

$$a^2 + b^2 = \frac{8^2 + 6^2}{2}$$​​


$$a^2 + b^2 = \frac{64 + 36}{2} = 50$$​​

Step 3: Solve for b :

We know a = 5 , so:

$$5^2 + b^2 = 50$$​​

$$25 + b^2 = 50$$​​

$$b^2 = 25$$​​

$$b = \sqrt{25} = 5$$​​

Correct Answer:

(B) 5