If the area of a parallelogram ABCD is 48 $c m^{2}$ , find the length of AD and AB, if OP = 8 cm and CQ = 12 cm.

3 cm, 2 cm

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6 cm, 4 cm

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8 cm, 6 cm

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12 cm, 8 cm

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Solution

The correct option is B 6 cm, 4 cm
OP = Height of the parallelogram corresponding to base CD.
CQ = Height of the parallelogram corresponding to base AD.

Area of parallelogram = base $\times$ height
48 = (AB or DC ) $\times$ OP
48 = (AB) $\times$ 8
AB = $\frac{48}{8}$ = 6 cm

Similarly,
Area of parallelogram = base $\times$ height
48 = AD $\times$ CQ
48 = AD $\times$ 12
AD = $\frac{48}{12}$ = 4 cm

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