find the area of Rhombus suicide 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 I need image illustrations also

Answer: The area of the rhombus is $24\text{ cm}^2$ and the length of the other diagonal is $6\text{ cm}$ .

Step-by-step solution

Step 1: Calculate the area of the rhombus using base and altitude

A rhombus is a special type of parallelogram with all equal sides. Therefore, its area can be calculated as the product of its base and corresponding altitude. Substituting base $= 5\text{ cm}$ and altitude $= 4.8\text{ cm}$ , we get an area of $24\text{ cm}^2$ .

Step 2: Set up the formula for area in terms of diagonals

The area of a rhombus can also be expressed in terms of the lengths of its diagonals as half the product of the diagonals, where $d_1$ and $d_2$ represent the lengths of the two diagonals.

Step 3: Calculate the length of the other diagonal

Equating the two expressions for the area gives $24 = \frac{1}{2} \times 8 \times d_2$ . Simplifying the right side gives $4 d_2 = 24$ . Dividing both sides by $4$ , we find the length of the second diagonal is $6\text{ cm}$ .

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