If the measure of a diagonal and the area of a rectangle are 25 cm and 168 cm$$^2$$ respectively, what is the length of the rectangle ?

Let the length and breadth of the rectangle be 'l' and 'b' respectively. Let 'd' be the diagonal of the rectangle.

$$ d^2 = l^2 + b^2 $$

$$ l^2 + b^2 = 625 $$

$$ l \times b = 168 $$

$$ (l + b)^2 = l^2 + b^2 + 2lb $$

Substituting,

$$ (l + b)^2 = 625 + 2 \times 168 = 961 $$

l + b = 31................(1)

$$ (l - b)^2 = l^2 + b^2 - 2lb $$

Substituting,

$$ (l - b)^2 = 625 - 2 \times 168 = 289 $$

l - b = 17.....................(2)

On solving (1) and (2)

l = 24