CAT Exam Model Paper 8 with solutions for free online practice

Question : 23 of 60

Marks: +1, -0

ABCD is a rectangle. Diagonals AC and BD intersect at point E. A perpendicular EF is drawn on AD from E. F and B are joined. FB and AE intersect at point G and a perpendicular GH is drawn on AD. H and B are joined. HB and AE intersect at I and a perpendicular IJ is drawn on AD. If AB = 10 cm, then what is the length of IJ (in cm)?

$4/5$
$5/2$
$5/4$
Cannot be determined

Validate

Solution:

{\EF}= { {\AB} ×{\CD}}/{ {\AB}+ {\CD}}= {10 × 10}/{10+10}=5 {\cm}

{GH}= { {\EF} ×{\AB}}/{ {\EF}+ {\AB}}= {5 ×10}/{10+5}= {10}/{3} {\cm}

{\IJ}= { {\HG} ×{\AB}}/{ {\GH}+ {\AB}}= {{10}/3×10}/{ {10}/{3}+10}= {5}/{2} {\cm}

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