Question

the perimeter of a rhombus is 40cm if one diagonal is 16 cm find its another diagonal and its area

Answer 1

Hola

Refer the attachment

Perimeter of Rhombus - 4a

a = sides of rhombus

Area of Rhombus = Pq/2

P and q are diagonals respectively.

Hope it helps

Answer 2

Answer:

• Length of other diagonal = 12 cm.

• Area of the Rhombus = 96 cm².

Step by step explanation:

[ Refer the attachment for figure. ]

Perimeter of Rhombus = 40 cm.

» Side = 1/4 × 40 = 10 cm.

One diagonal = 16 cm.

Diagonals of Rhombus bisect each other at right angles.

Now,

OB = √ (AB² - OA²)

= √ ( 10² - 8² )

= √ ( 100 - 64 )

= √ 36

= 6 cm.

Thus, Diagonal BD = 6 × 2 = 12 cm.

Now, Area of Rhombus = 1/2 × Product of diagonals

= 1/2 × 12 × 16

= 1/2 × 192

= 96 cm²

Hence, Area of Rhombus is 96 cm².

$\tt{Final \: \: answers: }$

Length of other diagonal = 12 cm.

Area of the Rhombus = 96 cm².