The distance between two side AB and CD of a rhombus ABCD is PQ and distance between sides AD and - Maths - Areas of Parallelograms and Triangles

Question

The distance between two side AB and CD of a rhombus ABCD is PQ and
distance between sides AD and BC is RS Let us prove that PQ=RS

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

Given: In a rhombus ABCD, ABor CD⊥PQ and BCor AD⊥RS
To prove: PQ=RSProof:As, area of rhombus ABCD=Base×Height=AB×PQ     
iAlso, area of rhombus ABCD=BC×RS                     
ii From i and ii, we getAB×PQ=BC×RSbut AB=BC   Sides of rhombus area equal∴ PQ=RS

Hope
this
information will clear
your doubts about the
topic
Regards

The distance between two side AB and CD of a rhombus ABCD is PQ and distance between sides AD and BC is RS. Let us prove that PQ=RS