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A triangle and a parallelogram have the same base and 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.

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Answer

Let a = 26 cm, b = 28 cm and c = 30 cm.

Semi-perimeter (s) = a+b+c2=26+28+302=842\dfrac{a + b + c}{2} = \dfrac{26 + 28 + 30}{2} = \dfrac{84}{2} = 42 cm.

Area of triangle = s(s−a)(s−b)(s−c)\sqrt{s(s - a)(s - b)(s - c)}

=42×(42−26)×(42−28)×(42−30)=42×16×14×12=112896=336 cm2.= \sqrt{42 \times (42 - 26) \times (42 - 28) \times (42 - 30)} \\[1em] = \sqrt{42 \times 16 \times 14 \times 12} \\[1em] = \sqrt{112896} \\[1em] = 336 \text{ cm}^2.

Since, area of parallelogram = area of triangle.

∴ Area of parallelogram = 336

⇒ base × height = 336

⇒ 28 × height = 336

⇒ height = 33628=12\dfrac{336}{28} = 12 cm.

Hence, height of parallelogram = 12 cm.

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