Question

In $\Delta ABC,$ segments $AD,BE$ and $CF$ 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: $AB\times AC=28.8$ and $BE\times CF=20$

$\Rightarrow AB=\frac{28.8}{AC}$ and $CF=\frac{20}{BE}$

Since $AB\perp CF$

$\Rightarrow AB\times CF=AC\times BE=BC\times AD=x$

i.e. $x=\frac{28.8\times 20}{x}$

$\Rightarrow x^2=576$

$\Rightarrow x=24$