In the triangle abc, the height an = 24 in, bn = 18 in, ac = 40 in. find ab and bc.

Step-by-step

AN is height, so A is perpendicular to BC.  (See image attached).

BN = 18

AN = 24

AC = 40

All as labeled.

ABN is a right triangle, with AB = sqrt(18^2+24^2)=sqrt(324+576)=30

ACN is a right triangle, with CN = sqrt(40^2-24^2)=sqrt(1600-576) = 32

=>

BC = BN + NC = 18 + 32 = 50

there will be 35 boys in each team. : )