In displaystyle 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-24-424-224-023-8

Question

Toppr Admin · Accepted Answer

Given- AB-xD7-AC-28-8 and-xA0-BE-xD7-CF-20-xA0-x21D2-AB-28-8AC and CF-20BESince AB-x22A5-CF-xA0-x21D2-AB-xD7-CF-AC-xD7-BE-BC-xD7-AD-xi-e- x-28-8-xD7-20x-x21D2-x2-576-x21D2-x-24

In $Δ A B C,$ segments $A D, B E$ and $C F$ are the altitudes. If $A B \times A C = 28.80$ and $B E \times C F = 20,$ then $A D \times B C$ equals:
$24.4$
$24.2$
$24.0$
$23.8$

Given: $A B \times A C = 28.8$ and $B E \times C F = 20$
$\Rightarrow A B = \frac{28.8}{A C}$ and $C F = \frac{20}{B E}$
Since $A B ⊥ C F$
$\Rightarrow A B \times C F = A C \times B E = B C \times A D = x$
i.e. $x = \frac{28.8 \times 20}{x}$
$\Rightarrow x^{2} = 576$
$\Rightarrow x = 24$

In ΔABC, segments AD,BE and CF are the altitudes. If AB×AC=28.80 and BE×CF=20, then AD×BC equals:24.424.224.023.8

Given: AB×AC=28.8 and BE×CF=20 ⇒AB=28.8AC and CF=20BESince AB⊥CF ⇒AB×CF=AC×BE=BC×AD=xi.e. x=28.8×20x⇒x2=576⇒x=24

In $Δ A B C,$ segments $A D, B E$ and $C F$ are the altitudes. If $A B \times A C = 28.80$ and $B E \times C F = 20,$ then $A D \times B C$ equals:
$24.4$
$24.2$
$24.0$
$23.8$

Given: $A B \times A C = 28.8$ and $B E \times C F = 20$
$\Rightarrow A B = \frac{28.8}{A C}$ and $C F = \frac{20}{B E}$
Since $A B ⊥ C F$
$\Rightarrow A B \times C F = A C \times B E = B C \times A D = x$
i.e. $x = \frac{28.8 \times 20}{x}$
$\Rightarrow x^{2} = 576$
$\Rightarrow x = 24$