Question

The perimeter og a triangle is 40 cm and its area 60 cm if the largest

Answer 1

a+b+a2+b2−−−−−−√=40a+b−40=−a2+b2−−−−−−√(a+b)2−80(a+b)+1600=a2+b22ab−80(a+b)+1600=0240−80(a+b)+1600=0a+b=23a+b+a2+b2=40a+b−40=−a2+b2(a+b)2−80(a+b)+1600=a2+b22ab−80(a+b)+1600=0240−80(a+b)+1600=0a+b=23

So a+b=23a+b=23, ab=120ab=120 and aa and bb have to satisfy the quadratic equation

x2−23x+120=0x2−23x+120=0

with solution

x1,2=12(23±529−480−−−−−−−−√)x1,2+12(23±49−−√)x1,2=12(23±529−480)x1,2+12(23±49)

So a=15,b=8,c=17