CAT Exam Model Paper 6 with solutions for free online practice

Question : 21 of 60

Marks: +1, -0

In a square PQRS, T is the midpoint of PQ and U is any variable point on QR. What is the minimum possible value of "SU + UT’ (in cm) if the side of the square is 2 cm?

$2√2$
$√5+√2$
$1+2√2$
$√13$

Validate

Solution:

Let us take a projection of the square PORS about the edge QR as shown below:

Using projection of the figure through a mirror image we can see that:
TU + US = TU + US’
Minimum value of (TU + US') will be when the points T, U and S’ lie on a straight line. In that case
TU + US' = TS'

= √{ ( 3 ) ^ { 2 } + ( 2 ) ^ { 2 } } = √{ 9 + 4 } =√ { 13 }

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