Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram?


Answer :

Let ABC be a triangle with sides AB = 26 cm, BC = 28 cm, CA = 30 cm

image

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.

NCERT solutions of related questions for Heron's Formula

NCERT solutions of related chapters class 9 maths

NCERT solutions of related chapters class 9 science