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.

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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.

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Detailed Solution

Side = 5 cm

Altitude = 4.8 cm

Length of one diagonal = 8 cm

Area of the rhombus $= S i d e \times A l t i t u d e = 5 \times 4.8 = 24 c m^{2}$

Area of the rhombus $= \frac{1}{2} \times d_{1} \times d_{2}$
$24 = \frac{1}{2} \times d_{1} \times d_{2}$
$24 = 4 \times d_{2}$
$d_{2} = 6 c m$
Hence, the length of other diagonal = 6 cm.