The area of a rhombus is 48 square cm and one diagonal is 8 cm. What is the leng

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Question: The area of a rhombus is 48 square cm and one diagonal is 8 cm. What is the length of the other diagonal?

Options:

Correct Answer: 12 cm

Solution:

Area = (1/2) × d1 × d2. Thus, 48 = (1/2) × 8 × d2, giving d2 = 12 cm.

The area of a rhombus is 48 square cm and one diagonal is 8 cm. What is the length of the other diagonal?

The area of a rhombus is 48 square cm and one diagonal is 8 cm. What is the length of the other diagonal?

Step 1: Understand that the area of a rhombus can be calculated using the formula: Area = (1/2) × d1 × d2, where d1 and d2 are the lengths of the diagonals.
Step 2: Identify the values given in the problem. The area is 48 square cm and one diagonal (d1) is 8 cm.
Step 3: Substitute the known values into the area formula: 48 = (1/2) × 8 × d2.
Step 4: Simplify the equation. First, calculate (1/2) × 8, which equals 4. So, the equation becomes: 48 = 4 × d2.
Step 5: To find d2, divide both sides of the equation by 4: d2 = 48 / 4.
Step 6: Calculate the result: d2 = 12 cm.

Area of a Rhombus – The area of a rhombus can be calculated using the formula Area = (1/2) × d1 × d2, where d1 and d2 are the lengths of the diagonals.
Properties of Diagonals – In a rhombus, the diagonals bisect each other at right angles, which is important for understanding their relationship.