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Answer :
Let ABC be a triangle with sides AB = 26 cm, BC = 28 cm, CA = 30 cm
Now, we know that,
\(s = \frac{AB + BC + CA}{2}\)
\(\therefore \) \(s = \frac{26 + 28 + 30}{2} = \frac{84}{2} = 42cm\)
Now, Area of triangle
= \(\sqrt{42(42 - 26)(42 - 28)(42 - 30)}\)
(Since, Heron's formula [area = \(\sqrt{s(s - a)(s - b)(s - c)}\)])
= \(\sqrt{42 × 16 × 14 × 12}\)
= \(\sqrt{7 × 6 × 4 × 4 × 2 × 7 × 2 × 6}\)
= \(7 × 6 × 4 × 2 {cm}^2\)
= \(336 {cm}^2\) ...(i)
We know that,
Area of parallelogram = Base × Height ...(ii)
We also have,
Area of parallelogram = Area of \(\triangle{ABC}\) ...(Given)
Thus, from (i) and (ii),
\(\Rightarrow \) Base × Height = 336
\(\Rightarrow \) 28 × Height = 336 ...(Given)
\(\Rightarrow \) Height = 12cm
Therefore, the height of the parallelogram is 12cm.