Question

the length of a wooden frame is 1 foot longer than is width and its area is equal to 12 ft2

Answer 1

The length and width of the wooden frame is 4 ft. and 3 ft. respectively.

Here, according to the given information, we are given that,

The length of the given wooden frame is 1 foot longer than its width.

Now, if we consider that the width of the wooden frame is x ft. Then, by the given information, we can say that, the length of the wooden frame is,

(x + 1) ft.

Now, area of the wooden frame is given as, 12 ft².

We know that, the area of a rectangle is equal to length multiplied by its width.

Now, placing the values in the formula of the area of a rectangle, we get,

$x.(x+1) = 12$.

Or, $x^{2} +x-12=0$

Or, $x^{2} +4x-3x-12=0$

Or, $x(x+4) -3(x+4)=0$

Or, $(x-3)(x+4) = 0$

Then, x is either 3 or -4.

Since the dimensions of both length or width cannot be negative, we take the positive value of x.

Then, x = 3 and x + 1 = 4.

Hence, the length and width of the wooden frame is 4 ft. and 3 ft. respectively.

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