Question

Prelungirile laturilor nepararele AD si BC ale unui trapez ABCD se intersecteaza in M. Stiind ca AB=15 cm, AD=6cm, BC=8 cm si CD= 5cm , sa se calculeze perimetrul triunghiului MDC

Answer 1

ABCD-trapez
AD intersectat BC ={M}  <=> ΔMDC ≈ MAB  =>TFa

MD/AM=MC/MB=DC/AB <=>

<=> MD/(MD+AD) =MC/(MC+BC) = 5/15 <=>

<=> MD/(MD+6) = MC/(MC+8)= 1/3  <=>

MD/(MD+6)=1/3

3MD=MD+6

3MD-MD=6

2MD=6

MD=3

MC/(MC+8)=1/3

3MC=MC+8

3MC-MC=8

2MC=8

MC=4

P ΔMDC= MD+MC+DC= 3+4+5= 12