In an isosceles $△ J K L$ , $J L = 26, M N : M P$ is $8 : 5$ , then the length of $J M$ is:

8

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16

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24

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4

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Solution

The correct option is B $16$
Since the triangle is given to be isosceles, assuming that $J K = L K$ , we get $∠ K J L = ∠ K L J$
$Δ J N M \sim Δ L P M$ since all the angles of both triangles are the same.
$∴ \frac{M N}{M P} = \frac{J M}{M L}$
$\Rightarrow \frac{8}{5} = \frac{J M}{M L}$
$\Rightarrow J L = J M + M L = J M + \frac{5}{8} J M$
$\Rightarrow J L = \frac{13}{8} J M$
$\Rightarrow J M = 26 \times \frac{8}{13} = 16$

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In an isosceles △JKL, JL=26,MN:MP is 8:5, then the length of JM is:

The correct option is B 16Since the triangle is given to be isosceles, assuming that JK=LK, we get ∠KJL=∠KLJΔJNM∼ΔLPM since all the angles of both triangles are the same.∴MNMP=JMML⇒85=JMML⇒JL=JM+ML=JM+58JM⇒JL=138JM⇒JM=26×813=16

In an isosceles $△ J K L$ , $J L = 26, M N : M P$ is $8 : 5$ , then the length of $J M$ is: