Hello,

let l be the length of the rectangle

and r be the radius of the circle then you get the equations according to your problem:

(Unfortunately the Latex isn't working anymore. So I repeat my equations in plain text)

equ(1): A_{rectangle}-A_{circle}: l * 2r - π* r^2=126

equ(2): p_{rectangle}+p_{circle}: 2l+4r+2πr=112

Now calculate l from equ(1) using π = 22/7 : l = (126+22/7*r^2)/(2r)

and put this term into equ(2) instead of l:

2*(126+22/7*r^2)/(2r) +4r+2πr=112

After a few transformation you'll get a quadratic equation:

94r^2 - 784r + 882 = 0

which has 2 solutions: r = 7 or r = 63/47

Now plug in these values to calculate l. You get:

l = 20 or l = 2308/47

EB