Question

The perimeter of a rectangle is 42, and its diagonal is 15. Find its length and width.
length _____(larger side)
width ______(smaller side)

Answer 1

Rectangle perimiter:
2(a+b)=42 ; a+b=21 ; b=21-a

Pythagoras:
a^2+b^2=15^2
a^2+(21-a)^2-225=0
a^2-21a+108=0

Two solutions:
a1 = 9 ; b=21-9 = 12
a2=12 ; b=21-12 = 9

So length=12, width=9