ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

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Detailed Solution

Given: AB = 16 cm, AE = 8 cm, CF = 10 cm

In parallelogram ABCD, CD = AB = 16 cm [Opposite sides of a parallelogram are equal]

We know that area of a parallelogram = Base × Corresponding altitude

Therefore, Area of parallelogram ABCD = CD × AE = AD × CF

Here CD and AD act as the base and AE ⊥ CD, CF ⊥ AD are the corresponding altitudes.

∴ AD = (CD × AE) / CF

Substituting the values for CD, AE, and CF, we get AD = (16 × 8) /10 cm = 12.8 cm

Thus, the length of AD is 12.8 cm.

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