Question

In the given figure, seg XY || seg AC. If 3 AX = 2 BX and XY = 9. Find length of AC. ​

Answer 1

this is the answer

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Answer 2

Given :

• Seg XY $\parallel$ seg AC.
• 3AX = 2BX.
• XY = 9

To Find :

• Length of AC.

Solution :

3AX = 2 BX.

•°• $\mathtt{\dfrac{AX}{BX}}$ = $\mathtt{\dfrac{2}{3}}$

✪ By componendo,

➟ $\mathtt{\dfrac{AX+BX}{BX}\:=\:{\dfrac{2+3}{3}}}$

➟ $\mathtt{\dfrac{AB}{BX}\:=\:{\dfrac{5}{3}}}$

✪ By invertendo,

➟ $\mathtt{\dfrac{BX}{AB}\:=\:{\dfrac{3}{5}}}$ _____(1)

✪ In Δ BXY and Δ BAC,

➟ $\angle$ BXY $\cong$ $\angle$ BAC $\sf{\underbrace{Corresponding \:angles}}$

➟ $\angle$ XBY $\cong$ $\angle$ ABC

$\sf{\underbrace{Common \:angles}}$

•°• Δ BXY ~ Δ BAC ....( AA test)

•°• $\mathtt{\dfrac{BX}{AB}}$ = $\mathtt{\dfrac{XY}{AC}}$ = $\mathtt{\dfrac{BY}{BC}}$

✪ We have values of BX, AB, XY and we need to calculate AC.

Hence, choosing the suitable pair.

➟ $\mathtt{\dfrac{BX}{AB}}$ = $\mathtt{\dfrac{XY}{AC}}$

➟ $\mathtt{\dfrac{3}{5}}$ = $\mathtt{\dfrac{9}{AC}}$

➟ $\mathtt{3AC\:=\:45}$

➟ $\mathtt{AC\:=\:{\dfrac{45}{3}}}$

➟ $\mathtt{AC\:=\:15}$

$\large{\boxed{\mathtt{\red{Length\:of\:AC\:=\:15}}}}$