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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.

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- NCERT solutions for class 9 maths chapter 1 Number Systems
- NCERT solutions for class 9 maths chapter 2 Polynomials
- NCERT solutions for class 9 maths chapter 3 Coordinate geometry
- NCERT solutions for class 9 maths chapter 4 Linear equations in two variables
- NCERT solutions for class 9 maths chapter 5 Introduction to Euclidean Geometry
- NCERT solutions for class 9 maths chapter 6 Lines and Angles
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- NCERT solutions for class 9 maths chapter 11 Constructions
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- NCERT solutions for class 9 maths chapter 13 Surface areas and volumes
- NCERT solutions for class 9 maths chapter 14 Statistics
- NCERT solutions for class 9 maths chapter 15 Probability

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