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Question

ABC is a right angle triangle in which B=900 and BC=a. If n points L1, L2, ..., Ln on AB are such that AB divided in n+1 equal parts and L1M1, L2M2, ..., LnMn are line segments parallel to BC and M1, M2, ..., Mn are on AC then the sum of the lengths of L1M1, L2M2, ..., LnMn is

A
a(n+1)2
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B
a(n1)2
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C
an2
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D
impossible to find from given data
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Solution

The correct option is C an2
AL1AB=L1M1BC;1n+1=L1M1a;L1M1an+1
AL2AB=L2M2BC;2n+1=L2M2a;L1M22an+1,
the required sum
=an+1+2an+1+3an+1+...+nan+1
=an+1(1+2+3+...+n)=an+1.n(n+1)2=an2
360933_133573_ans.PNG

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