Multiple choice

A figure is in the form of a quadrilateral $ABCD$ its area is $165\;cm^2$. Find the length of the perpendicular drawn from $D$ on $AC$ if $AC=15\;cm$ and length of perpendicular from $B$ on $AC$ is $12\;cm$.

  1. $10\;cm$
  2. $20\;cm$
  3. $30\;cm$
  4. $40\;cm$
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A Correct answer
Explanation

Area of quadrilateral ABCD = Area(ADC) + Area(ABC). Area = (1/2) * AC * h1 + (1/2) * AC * h2 = (1/2) * AC * (h1 + h2). 165 = (1/2) * 15 * (h1 + 12). 165 = 7.5 * (h1 + 12). 22 = h1 + 12, so h1 = 10.

AI explanation

The area of a quadrilateral with perpendicular diagonals can be calculated using the formula Area = (1/2) * diagonal * (sum of perpendiculars). Substituting the given values into the formula, we get 165 = (1/2) * 15 * (12 + h). Solving this equation, 165 = 7.5 * (12 + h), we find that 22 = 12 + h, which gives a perpendicular length of 10 cm.

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