Question 963586
.
.
s=Side of square; W=width of rectangle=s+5cm; L=length of rectangle=W+4cm=s+9cm
Area of square=s^2; Area of rectangle=(L)(W)
Total Area=area of square + area of rectangle
{{{201cm^2=s^2+(L)(W)}}}
{{{201cm^2=s^2+(s+9cm)(s+5cm)}}}
{{{201cm^2=s^2+s^2+14s+45)}}}
{{{0=2s^2+14s-156}}}
{{{0=s^2+7s-78}}}
{{{0=(s+13)(s-6)}}}
{{{s+13=0}}} or {{{s-6=0}}}
{{{s=-13}}} {{{or}}} {{{s=6}}}
ANSWER 1: The sides of the square are 6 cm
{{{W=s+5cm}}}={{{6cm+5cm=11cm}}} ANSWER 2: The width of the rectangle is 11 cm.
{{{L=W+4cm}}}={{{11cm+4cm=15cm}}} ANSWER 3: The length of the rectangle is 15 cm.
CHECK:
Total Area = area of square + area of rectangle
{{{201cm^2=s^2+(L)(W)}}}
{{{201cm^2=(6cm)^2+(11cm)(15cm)}}}
{{{201cm^2=36cm^2+165cm^2}}}
{{{201cm^2=201cm^2}}}