A rectangular piece of cardboard measure 17cm by 14cm. Strips of equal width are cut off one side and one End. The area of the remaining piece is 108cm² find the width of the strips removed

Let the width of the strips cut off from one side and one end be ( x ) cm.

After cutting off the strips, the dimensions of the remaining piece are:

• Length: ( 17 - x ) cm
• Width: ( 14 - x ) cm

The area of the remaining piece is given by:

[ (17 - x)(14 - x) = 108 ]

Now, let's expand this equation:

[ 238 - 17x - 14x + x^2 = 108 ]

Simplifying it, we obtain:

[ x^2 - 31x + 238 - 108 = 0 ]

[ x^2 - 31x + 130 = 0 ]

Next, we can solve this quadratic equation using the quadratic formula:

[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} ]

Here, ( a = 1 ), ( b = -31 ), and ( c = 130 ).

Calculating the discriminant:

[ b^2 - 4ac = (-31)^2 - 4 \cdot 1 \cdot 130 = 961 - 520 = 441 ]

Now substituting back into the quadratic formula:

[ x = \frac{{31 \pm \sqrt{441}}}{2} = \frac{{31 \pm 21}}{2} ]

Calculating the two possible values for ( x ):

1. ( x = \frac{{31 + 21}}{2} = \frac{52}{2} = 26 )
2. ( x = \frac{{31 - 21}}{2} = \frac{10}{2} = 5 )

Since ( x = 26 ) cm is not possible (as it exceeds the small side of the cardboard), we have:

[ x = 5 \text{ cm} ]

Thus, the width of the strips removed is ( \boxed{5} ) cm.