Question

In $\Delta ABC$, segments $AD,BEandCF$ are the altitudes. If $AB\times AC=28.80$ and $BE\times CF=20$, then $AD\times BC$ equals

• A. $24.4$
• B. $24.2$
• C. $24.0$
• D. $23.8$

Answer 1

The correct option is C $24.0$

Given AB * AC = 28.8 and BE * CF = 20
Multiplying the above 2 equations we get,
AB * AC * BE * CF = 576
Re-grouping the terms, (AB * CF) * (AC * BE) = 576
Now, AB * CF = 2 * area of a triangle [area of a triangle = 0.5 * base * ht]
Similarly, AC * BE = 2 * area of a triangle [area of a triangle = 0.5 * base * ht]
(AB * CF) * (AC * BE) = 576 [square of double the area of triangle]
So, double the area of triangle = 24 [taking the square root]
Therefore, AD * BC = 24. [AD * BC = 2 * area of triangle]