Question

Two squares have side lengths that are consecutive odd integers. The total area of the squares is 650cm^2. What is their total perimeter?

Answer 1

`the\ consecutive\ odd\ integers\ is:2n+1\ and\ 2n+3\ (n\in\mathbb{N})\\\\Area_1=(2n+1)^2=4n^2+4n+1\\\\Area_2=(2n+3)^2=4n^2+12n+9\\\\Area_1+Area_2=4n^2+4n+1+4n^2+12n+9=8n^2+16n+10\\\\8n^2+16n+10=650\\\\8n^2+16n+10-650=0\\\\8n^2+16n-640=0\ \ /:8`


`n^2+2n-80=0\\\\\Delta=2^2-4\cdot1\cdot(-80)=4+320=324;\ \sqrt\Delta=√(324)=18\\\\n_1=(-2-18)/(2\cdot1) < 0;\ n_2=(-2+18)/(2\cdot1)=(16)/(2)=8\\\\2n+1=2\cdot8+1=16+1=17\ (m)\\\\2n+3=2\cdot8+3=16+3=19\ (m)\\\\\\the\ total\ perimeter=4\cdot17+4\cdot19=68+76=144\ (m)`