If $p^{2} + 6 p - 16$ is the possible expression for the area of rectangle, find its length and breadth.

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Solution

Given $p^{2} + 6 p - 16$ is represents area of rectangle then
We know
area of rectangle = length $\times$ breadth = $l \times b$
$l \times b = p^{2} + 6 p - 16$
$l \times b = p^{2} + 8 p - 2 p - 16$
$l \times b = p (p + 8) - 2 (p + 8)$
$l \times b = (p + 8) (p - 2)$
on comparing we get length of rectangle is (p+8) and breadth is (p-2) respectively.

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