Question

PQRS is a photoframe in the shape of a quadrilateral in which QR=3cm , PR=11cm,RS=4cm, PS=3cm, then the minimum integral possible value of PQ is ______. Give reason to support your answer.

Answer 1

Step-by-step explanation:

In figure ST || QR

and PS= 3 cm & RS= 4cm

In ΔPST & PQR

QPR=∠TPS [Common]

∠PRQ=∠PST [corresponding]

ΔPQR∼ΔPST [AA similarity]

Now

In similar triangles ratios of the area of triangles is equal to the ratio of the square of corresponding sides.

Ar. ofΔPRQ

Ar.ofΔPST

(

3+4

3

)

2

=

49

9

Hence [

Ar.ofΔPRQ

Ar.ofΔPST

=

49

9

]