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Mathematics

The area of a parallelogram is 98 cm2. If one altitude is half the corresponding base, determine the base and the altitude of the parallelogram.

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Answer

Let base = x cm

Corresponding altitude = x2\dfrac{x}{2} cm

By formula,

Area of parallelogram = base × altitude

Substituting the values we get,

⇒ 98 = x×x2x \times \dfrac{x}{2}

⇒ 98 = x22\dfrac{x^2}{2}

⇒ x2 = 98 × 2 = 196

⇒ x = 196\sqrt{196} = 14 cm

⇒ Base = x = 14 cm

⇒ Altitude = x2\dfrac{x}{2} = 7 cm.

Hence, base = 14 cm and altitude = 7 cm.

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