Question Number 10006 by RasheedSoomro last updated on 20/Jan/17

A triangle is divided into four triangles  and three quadrilaterals by three straight  line segments(for figure see comment below).     ^• The sum of the perimeters of the three quadri-  laterals is 25 cm.   ^• The sum of the perimeters of the four triangles  is 20 cm.   ^• The perimeter of the whole triangle  is 19 cm.   ^• What is the sum of the lengths of the three  straight line segments?

Commented byRasheedSoomro last updated on 20/Jan/17

Answered by mrW1 last updated on 21/Jan/17

Q=(sum of the perimeters of the three quadrilaterals)  T=(sum of the perimeters of the four triangles)  P=(perimeter of the whole triangle)  S=(sum of the lengths of the three straight line segments)  Q+T=P+2S  S=((Q+T−P)/2)=((25+20−19)/2)=13 cm