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Question
The area of a rhombus is 240 cm2 and one of the diagonal is 16 cm. Find another diagonal.
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Solution
Given:
Area of the rhombus = 240 cm
Length of one of its diagonals = 16 cm
We know that if the diagonals of a rhombus are `d_1` and `d_2` , then the area of the rhombus is given by:
Area \[= \frac{1}{2}( d_1 \times d_2 )\]
Putting the given values:
\[240 = \frac{1}{2}(16 \times d_2 )\]
\[240 \times 2 = 16 \times d_2 \]
This can be written as follows:
\[16 \times d_2 = 480\]
\[ d_2 = \frac{480}{16}\]
\[ d_2 = 30 cm\]
Thus, the length of the other diagonal of the rhombus is 30 cm.
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