o observe the below figure in a spa, if ABII QR and PA=X-2, A2=X+5,PB=X-3 and BR=x+3 then find the value of a X
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In the given figure LM∣∣AB. If AL=x−3, AC=2x, BM=x−2 and BC=2x+3, find the value of x.
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In △ABC, we have
LM∣∣AB
∴
LC
AL
=
MC
BM
[By Thaley's Theorem]
⇒
AC−AL
AL
=
BC−BM
BM
⇒
2x−(x−3)
x−3
=
(2x+3)−(x−2)
x−2
⇒
x+3
x−3
=
x+5
x−2
⇒ (x−3)(x+5)=(x−2)(x+3)
⇒ x
2
+2x−15=x
2
+x−6
⇒ x=9
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