Question

PQRS is a rhombus with PR as a diagonal prove that 4PQ is greater than 2PR...

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solve fast pls pls pls pls ....​

Answer 1

°•° PQRS is a rhombus •°• PQ = RS = RQ = SP = x [say]-----(3)

now ,for a Δ to exist it must hv sum of 2 sides > 3rd side

applying this in Δ SPR

SR + SP > PR ----- (1)

applying this in Δ PRQ

PQ + RQ > PR ----(2)

by (1) & (2)

PQ + RQ > PR

SR + SP > PR

PQ + SR + RQ+ SP > PR +PR

=> x+x+x+x > 2PR

=> 4x > 2PR

=> 4 PQ > 2 PR [by (3) all sides are same i.e. x]

•°• 4 PQ > 2 PR

proved