The lengths of the diagonals of a parallelogram are 10√3 cm and 10�

1.	The lengths of the diagonals of a parallelogram are 10√3 cm and 10√2 cm. If one side of the parallelogram is 13 cm, find the perimeter of the parallelogram.
Answer» Split the PARALLELOGRAM into 2 triangles (See ATTACHMENT) FIND the area of one triangle: Perimeter = 11 + 13 + 20 = 44 cm Semi-Perimeter = 44 ÷ 2 = 22 cm Area = √p(p - a)(p - b) (p - c) Area = √22(22 - 11)(22 - 13)(22 - 20) Area = √4356 Area = 66 cm² Find the area of the parallelogram: parallelogram = 2 x area of triangle Area = 66 x 2 = 132 cm² Find the other diagonal: Let the other diagonal be x 1/2 (diagonal 1 x diagonal 2) = Area 1/2 (20x) = 132 10x = 132 x = 13.2 cm Answer: The other diagonal is 13.2 cm

The lengths of the diagonals of a parallelogram are 10√3 cm and 10√2 cm. If one side of the parallelogram is 13 cm, find the perimeter of the parallelogram.

Answer»

Split the PARALLELOGRAM into 2 triangles (See ATTACHMENT)

FIND the area of one triangle:

Perimeter = 11 + 13 + 20 = 44 cm

Semi-Perimeter = 44 ÷ 2 = 22 cm

Area = √p(p - a)(p - b) (p - c)

Area = √22(22 - 11)(22 - 13)(22 - 20)

Area = √4356

Area = 66 cm²

Find the area of the parallelogram:

parallelogram = 2 x area of triangle

Area = 66 x 2 = 132 cm²

Find the other diagonal:

Let the other diagonal be x

1/2 (diagonal 1 x diagonal 2) = Area

1/2 (20x) = 132

10x = 132

x = 13.2 cm

Answer: The other diagonal is 13.2 cm

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The lengths of the diagonals of a parallelogram are 10√3 cm and 10√2 cm. If one side of the parallelogram is 13 cm, find the perimeter of the parallelogram.​

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The lengths of the diagonals of a parallelogram are 10√3 cm and 10√2 cm. If one side of the parallelogram is 13 cm, find the perimeter of the parallelogram.