Question

I really dont understand this so please help

Answer 1

`\mathrm{Solution:}\\\mathrm{Here,\ we\ use\ pythagoras\ theorem\ in\ three\ right\ angled\ triangles\ DEG, EFG}\\\mathrm{and\ FED.}\\`

`\mathrm{In\ \triangle DEG,}\\\mathrm{DE^2=EG^2+DG^2}\\\mathrm{or,\ DE^2=EG^2+a^2}\\\mathrm{or,\ DE^2=EG^2+16}\\\mathrm{In\ \triangle EFG,}\\\mathrm{EF^2=EG^2+GF^2}\\\mathrm{or,\ EF^2=EG^2+b^2}\\\mathrm{or,\ EF^2=EG^2+144}\\\mathrm{Now,}\\\mathrm{In\ \triangle FED,}\\\mathrm{FD^2=DE^2+EF^2}\\\mathrm{or,\ (DG+GF)^2=(EG^2+16)+(EG^2+144)}\\\mathrm{or,\ (4+12)^2=2EG^2+160}\\\mathrm{or,\ 256=2EG^2+160}\\\mathrm{or,\ 96=2EG^2}\\\mathrm{or,\ EG^2=48}\\\mathrm{or,\ EG=4\sqrt3}`