Question

The perimeter of a rhombus is 146cm and one of its diagonals is 55cm. find the other diagonal and the area of the rombhus.​

Answer 1

Answer:

48 cm

Step-by-step explanation:

Find the length of one side:

Perimeter = 146 cm

Length = Perimeter ÷ 4

Length = 146 ÷ 4 = 36.5 cm

Find 1/2 of the known diagonal:

1/2 of the diagonal = 55 ÷ 2 = 27.5 cm

Find 1/2 of the other diagonal:

Let 1/2 of the other diagonal be x

a² + b² = c²

x² + 27.5² = 36.5²

x² = 36.5² - 27.5²

x² = 576

x = 24

Find the length of the other diagonal:

1/2 the length = 24 cm

the length = 24 x 2 = 48 cm