Question : A triangle and a parallelogram have the same base 28 cm and the same area. If the height of the parallelogram is 12 cm, then find the length of the altitude of the triangle.
Option 1: 28 cm
Option 2: 23 cm
Option 3: 24 cm
Option 4: 21 cm
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Correct Answer: 24 cm
Solution :
Area of the parallelogram = $28 \times 12 = 336\ \mathrm{cm^2}$
Let the length of the altitude of the triangle be $h$ cm.
According to the question,
$\frac{1}{2}\times h \times 28 = 336$
⇒ $h = 12\times2$
⇒ $h = 24\text{ cm}$
Hence, the correct answer is 24 cm.
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