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Question
Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
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Solution
Given:
Side of the rhombus = 6 cm
Altitude = 4 cm
One of the diagonals = 8 cm
Area of the rhombus = Side x Altitude \[= 6 x 4 = 24 {cm}^2 . . . . . . . . (i)\]
We know: Area of rhombus \[= \frac{1}{2} \times d_1 \times d_2 \]
Using (i):
\[24 = \frac{1}{2} \times d_1 \times d_2 \]
\[24 = \frac{1}{2} \times 8 \times d_2 \]
\[ d_2 = 6 cm\]
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