Question

ABCD is a parallelogram whose daigonals intersect each other at right angles if the length of the diagonals is 6 cm and 8 cm find the length of all the sides of the parallelogram.​

Answer 1

Answer:

★Length of all sides will be 5 cm ★

Step-by-step explanation:

Given:

• ABCD is a parallelogram whose diagonals intersect each other at O at right angles

• Length of Diagonals are 6 cm and 8 cm

To Find:

• Length of all sides of the parallelogram

Solution: In parallelogram ABCD

→ AC ( Diagonal) = 6 cm

∴ AO = 1/2 AC = 1/2 x 6 = 3cm

∴ OC = 1/2 AC = 1/2 x 6 = 3cm

→ BD ( Diagonal) = 8 cm

∴ OB = 1/2 BD = 1/2 x 8 = 4cm

∴ OD = 1/2 BD = 1/2 x 8 = 4cm

★Also we can apply Pythagoras Theorem in the given triangles because they all are at 90° ★

→ In ∆ BOC, By Pythagoras Theorem,

$\small\implies{\sf }$ BC² = BO² + OC²

$\small\implies{\sf }$ BC² = 4² + 3²

$\small\implies{\sf }$ BC² = 16 + 9 = 25

$\small\implies{\sf }$ BC = √25 = 5 cm

★Similarly in ∆ BOA, By Pythagoras Theorem we will get AB = 5 Cm

† We know that the Opposite Sides of a Parallelogram are equal and parallel †

∴ AB = DC = 5 cm

∴ BC = AD = 5 cm

Hence, Length of the all sides of the Parallelogram will be 5 Cm.