hello help me with this question thanks in advance​

[tex]\bold{\huge{\underline{ Solution\: C }}}[/tex]

Here,

By using basic proportionality theorem

[tex]\sf{\dfrac{ x }{ x + 16 }}{\sf{=}}{\sf{\dfrac{9}{12 + 9}}}[/tex]

By cross multiplication ,

[tex]\sf{ 21x = 9( x + 16)}[/tex]

[tex]\sf{ 21x = 9x + 144}[/tex]

[tex]\sf{ 21x - 9x = 144}[/tex]

[tex]\sf{ 12x = 144}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{ 144}{12}}}[/tex]

[tex]\bold{ x = 12}[/tex]

Hence, The value of x is 12

Here also ,

By using basic proportionality theorem :-

[tex]\sf{\dfrac{ 4 }{ 4 + 10 }}{\sf{=}}{\sf{\dfrac{6}{x +6}}}[/tex]

[tex]\sf{\dfrac{ 4 }{ 14 }}{\sf{=}}{\sf{\dfrac{6}{x +6}}}[/tex]

By cross multiplication ,

[tex]\sf{ 4(x + 6) = 6 {\times} 14}[/tex]

[tex]\sf{ 4x + 24 = 84}[/tex]

[tex]\sf{ 4x = 84 - 24}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{ 60}{4}}}[/tex]

[tex]\bold{ x = 15}[/tex]

Hence, The value of x is 15 .

[tex]\bold{\huge{\underline{ Solution\: D }}}[/tex]

Here,

In triangle JHL and In triangle JKL

By using similarity theorem

[tex]\sf{\dfrac{ JH }{ JK}}{\sf{=}}{\sf{\dfrac{HL}{KL}}}[/tex]

Subsitute the required values,

[tex]\sf{\dfrac{ 12 }{ 15 }}{\sf{=}}{\sf{\dfrac{18}{KL}}}[/tex]

By cross multiplication

[tex]\sf{ 12( KL) = 18 {\times} 15}[/tex]

[tex]\sf{ 12(KL) = 270}[/tex]

[tex]\sf{ KL = }{\sf{\dfrac{ 270}{12}}}[/tex]

[tex]\bold{ KL = 22.5 }[/tex]

Hence, The length of KL is 22.5

Here also,

In triangle JHL and In triangle JKL

By using similarity theorem :-

[tex]\sf{\dfrac{ JH }{ JK}}{\sf{=}}{\sf{\dfrac{HL}{KL}}}[/tex]

Subsitute the required values,

[tex]\sf{\dfrac{ 14 }{ 20}}{\sf{=}}{\sf{\dfrac{HL}{6}}}[/tex]

[tex]\sf{\dfrac{ 7 }{ 10}}{\sf{=}}{\sf{\dfrac{HL}{6}}}[/tex]

[tex]\sf{\dfrac{ 7 }{ 10}}{\sf{{\times} 6= HL }}[/tex]

[tex]\sf{\dfrac{ 7 }{ 5 }}{\sf{{\times} 3 = HL }}[/tex]

[tex]\sf{\dfrac{ 21 }{ 5}}{\sf{ = HL }}[/tex]

[tex]\bold{ HL = 4.2 }[/tex]

Hence, The length of HL is 4.2 .

HELP ASAP HELP ASAP


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