Question

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 1

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