Question

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

Answer 1

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 `2x+2y=10`

Since the area is 6, it implies that `xy=6`

We may now solve these 2 equations simultaneously to obtain :

`x+y=5 =>y=5-x`

`therefore x(5-x)=6 => x^2-5x+6=0`

Solving for x in this quadratic equation we get : `x=3 or 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.

Answer 2

If 'l' and 'b' are the length and breadth of a rectangle respectively then `perimeter= 2(l+b)` and `area=lb`.
So, `2(l+b)=10` ,or, `l+b=5`.
So `b=5-l`.
Therefore, `l*(5-l)=6`, or,
`l^2-5l+6=0`, or,
`l^2-3l-2l+6=0`, or,
`l(l-3)-2(l-3)=0`, or,
`l=2, l=3`.
Out of the 2 values of l, one is the length and the other is the breadth.