Question 1131888
The first thing I'd do is create a drawing.
*[illustration Drawing]
Next you need to know the equation of the diagonal of a shape (The Pythagorean theorem):
{{{d^2 = w^2 + h^2}}}
Meaning we can now write an equation to solve for x
{{{(x^2 + (x+7)^2) = 13^2}}}
{{{(x^2 + x^2 + 14x + 49) = 169}}}
{{{2x^2 + 14x - 120 = 0}}}
Since this is in standard form and equal to 0 we can use the quadratic formula: {{{(-b+- sqrt(b^2-4*a*c))/(2*a)}}}
{{{(-14+- sqrt(14^2-4*2*-120))/(2*2)}}}
Therefore:
{{{x = - 12}}} OR {{{x = 5}}}
Since a side length cannot be negative, we can "Throw away" the {{{x = -12}}}
Therefore: x = 5
Meaning the dimensions of the rectangle are 5 x 12