# The perimeter of a rectangle is 10 inches, and its area is 6 square inches. Find the length and width of the rectangle?

Oct 13, 2015

Length 3 units and width 2 units.

#### Explanation:

Let the length be $x$ and the width be $y$

Since perimeter is 10, it implies that $2 x + 2 y = 10$

Since the area is 6, it implies that $x y = 6$

We may now solve these 2 equations simultaneously to obtain :

$x + y = 5 \implies y = 5 - x$

$\therefore x \left(5 - x\right) = 6 \implies {x}^{2} - 5 x + 6 = 0$

Solving for x in this quadratic equation we get : $x = 3 \mathmr{and} x = 2$

If $x = 3$, then $y = 2$

If $x = 2$, then $y = 3$

Usually the length is considered to be longer than the width, so we take the answer as length 3 and width 2.

Oct 13, 2015

If 'l' and 'b' are the length and breadth of a rectangle respectively then $p e r i m e t e r = 2 \left(l + b\right)$ and $a r e a = l b$.
So, $2 \left(l + b\right) = 10$ ,or, $l + b = 5$.
So $b = 5 - l$.
Therefore, $l \cdot \left(5 - l\right) = 6$, or,
${l}^{2} - 5 l + 6 = 0$, or,
${l}^{2} - 3 l - 2 l + 6 = 0$, or,
$l \left(l - 3\right) - 2 \left(l - 3\right) = 0$, or,
$l = 2 , l = 3$.
Out of the 2 values of l, one is the length and the other is the breadth.