Question 429725
Solution:Let x cm the width, then the diagonal is x+9 cm, and the length of rectangle, using Pythagorean theorem will be:

{{{L^2=(x+9)^2-x^2=x^2+18x+81-x^2=18x+81}}}, and

{{{L=sqrt(18x+81)}}}

The perimeter of rectangle is:2L+2W=120 => L+W=60 Write the equation:

{{{sqrt(18x+81)+x=60}}} Solve the equation:

{{{sqrt(18x+81)=60-x}}}, squaring both sides have:

{{{18x+81=x^2-120x+3600}}}, set equation to zero.

{{{x^2-138x+3519=0}}}, solve the quadratic equation.

The roots that satisfy our problem is L=33.75 cm and W=26.34 cm.

Done.