Question

find the area of a rhombus whose side is 5 cm and whose altitude altitude is 4.8 CM if one of the diagonal is 8 cm long find the length of other diagonal​

Answer 1

The area of the rhombus with side 5 cm and altitude 4.8 cm is 24 cm2, and the length of the other diagonal is 6 cm.

Step-by-step explanation:

Let's draw the diagram of rhombus ABCD according to the given question.

Side of the rhombus = 5 cm

So, AB = BC = CD = DA = 5cm (Since all the sides of a rhombus are equal)

Area of a rhombus = Base × Height (Since, rhombus is also a parallelogram)

= 5 cm × 4.8 cm (Since, altitude = 4.8cm)

= 24 cm2

Also, 

Area of a rhombus = (Product of the digonals)/2

Let, DB = d1 = 8 cm and CA = d2.

Area of a rhombus = (d1 × d2)/2

⇒ (d1 × d2)/2 = 24

⇒ 8 × d2 = 48

⇒ d2 = 48/8

⇒ d2 = 6

Hence, AC = 6 cm.

Answer 2

Question-

Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

Answer-

Area of the rhombus = Base × Length = 5 cm × 4.8 cm = 24 cm²

Also,

   Area of rhombus = 1/2 × Product of its diagonals

⇒ 24 = 1/2 (AD × CB)

⇒ 24 = 1/2 (x × 8 cm)

⇒ x × 4 = 24

⇒ x = 24/4

⇒ x = 6 cm

Thus the length of the other diagonal is 6 cm