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.

A rhombus is a parallelogram in which all the four sides are equal. In the given question, we need to find the area of a rhombus whose side is 5 cm and altitude is 4.8 cm. After we calculate the area, we can find the length of the other diagonal.

Answer: 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.

Let us draw the diagram of rhombus ABCD, then find the area and the length of the other diagonal.

Explanation:

Observe the following figure of rhombus ABCD and the dimensions that are given in the question.

Side of the rhombus = 5 cm

So, AB = BC = CD = DA = 5 cm (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 the altitude = 4.8 cm)

= 24 cm²

Now, we can find the length of the second diagonal using the following formula.

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

Here, the length of one diagonal = d1 = 8 cm and we need to find the length of the other diagonal CA = d2. We know that the area of the rhombus is 24 cm². So, let us substitute the given values of diagonal 1 and the area in the formula.

Area of a rhombus = (d1 × d2)/2

⇒ (d1 × d2)/2 = 24

⇒ 8 × d2 = 48

⇒ d2 = 48/8

⇒ d2 = 6

Therefore, the length of the second diagonal, AC = 6 cm.

Thus, 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.