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In a right-angled triangle A B C ABC A BC , the altitude A B AB A B is 5 cm, and the base B C BC BC is 12 cm. P P P and Q Q Q are two points on B C BC...

CAT Medium Triangles Integer

Question

In a right-angled triangle

ABCABC
, the altitude
ABAB
is 5 cm, and the base
BCBC
is 12 cm.
PP
and
QQ
are two points on
BCBC
such that the areas of
△ABP\triangle ABP
,
△ABQ\triangle ABQ
, and
△ABC\triangle ABC
are in arithmetic progression. If the area of
△ABC\triangle ABC
is 1.5 times the area of
△ABP\triangle ABP
, the length of
PQPQ
, in cm, is:

Answer Format

Enter your answer as an integer value

cat 2023right-angled trianglearithmetic progressiongeometry problems

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