Question 979838
x, width
y, height
diagonal is a hypotenuse of right triangle with legs x and y.


{{{12+y=x}}}, and x, are the legs.
{{{x^2+y^2=60^2}}}-----Pythagorean Theorem, because Right Triangle;
{{{(12+y)^2+y^2=60^2}}}

{{{144+24y+y^2+y^2=3600}}}

{{{2y^2+24y+144=3600}}}

{{{y^2+12y+72=1800}}}

{{{y^2+12y+72-1800=0}}}

{{{y^2+12y-1728=0}}}


You can factorize the constant nonvariable term.
12*12*12=2*...... but if you don't want to check all of that, use discriminant.
{{{(12)^2-4*(-1728)=144+4*1728=7056=84^2}}}.


{{{y=(-12+84)/2}}}, based on formula for general solution to quadratic equation, jumping through a couple of steps.
{{{highlight(y=36)}}}.


Now find x.
{{{x=12+y}}}
{{{x=12+36}}}
{{{highlight(x=48)}}}.