Question 964079
L=side of large square; S=side of small square
{{{4L+4S=200cm}}}
{{{L+S=50cm}}}
{{{L=50cm-S}}} Use this to substitute for L.
{{{L^2=9S^2}}} Substitute for L.
{{{(50cm-S)^2=9S^2}}}
{{{2500-100S+S^2=9S^2}}} Subtract S^2 from each side.
{{{2500-100S=8S^2}}} Add 100S to each side.
{{{2500=8S^2+100S}}} Subtract 2500 from each side.
{{{0=8S^2+100S-2500}}}
*[invoke quadratic "x", 8, 100, -2500 ]
S=12.5 cm
L=50cm-12.5cm=37.5cm
ANSWER: Perimeter of large square=4(37.5cm)=150 cm
CHECK:
{{{L^2=9S^2}}}
{{{37.5^2=(9)(12.5^2)}}}
{{{1406.25=(9)(156.25)}}}
{{{1406.25=1406.25}}}