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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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6 cm

7 cm

8 cm

9 cm

answer is A.

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Detailed Solution

It is given area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm and one of its diagonals is 8 cm long.
Area of rhombus =

Base × Altitude

The side of the rhombus is given to be 5 cm
Let this side be the base. Also, the altitude given is 4.8 cm
Since rhombus is also a kind of parallelogram hence, we can write,

Area of rhombus = Base × Altitude Area of rhombus = 6 × 4 Area of rhombus = 24 cm 2 … (I)

The one of the diagonals is given to be

8 cm

i.e.,

d_{1}

= 8.
And the other diagonal be

d_{2}

.
Therefore, the area of rhombus is given as,
Area of rhombus

= 12 × d 1 × d 2

……(II)
Equating equation (I) and (II),

⇒ 12 × d × 1 d 2 = 24 ⇒ 12 × 8 × d 2 = 24 ⇒ 4 × d 2 = 24 ⇒ d 2 = 244 ⇒ d 2 = 6 c m

The length of the other diagonal is 6 cm.
Hence, option (1) is correct.

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