Question 130098
Let {{{x}}}= the width
The height will be {{{x + 10}}}
The area of the picture is then {{{x*(x + 10)}}}
Including the border, the width is {{{x + 5 + 5}}}
Including the border, the height is {{{x + 10 + 5 + 5}}}
{{{(x + 5 + 5)(x + 10 + 5 + 5) = 580 + x*(x + 10)}}}
{{{(x + 10)(x + 20) = 580 + x^2 + 10x}}}
{{{x^2 + 30x + 200 = 580 + x^2 + 10x}}}
{{{20x = 580 - 200}}}
{{{x = 19}}}
{{{x + 10 = 29}}}
The dimensions of the picture are 19 x 29
check answer:
Adding up the pieces of the border,
{{{580 = 2*5*19 + 2*5*29 + 4*5^2}}}
{{{580 = 190 + 290 + 100}}}
{{{580 = 580}}}
OK
The area of the border + picture is
{{{19 + 5 + 5)(29 + 5 + 5)}}}
{{{29*39 = 1131}}}
{{{1131 - 580 = 551}}}
{{{19*29 = 551}}}
OK