A rectangular piece of cardboard measures 17cm by 14cm. Strips of equal width are cut off one side and one end. The area of the remaining piece is 108cm^2. Find the width of the strips
(17-x)(14-x) = 108
Solve for x.
43.
x is 5 or 26 because of Factorization
(17-x)(14-x)=108
17(14-x)-(14-x)
Pls wat is the question
To find the width of the strips cut off from one side and one end of the rectangular cardboard, we can use the formula for the area of a rectangle:
Area = Length × Width.
Let's assume the width of the strips cut off is 'x'.
Initially, the cardboard measures 17cm by 14cm, so its area is:
17cm × 14cm = 238cm².
Then, strips of width 'x' are cut off one side and one end. Since two strips are cut off, the resulting length and width of the remaining piece will be decreased by '2x'.
So, the length of the remaining piece will be (17cm - 2x), and the width will be (14cm - x).
We are given that the area of the remaining piece is 108cm², so we can write the equation:
(17cm - 2x) × (14cm - x) = 108cm².
Expanding the equation, we get:
238cm² - 17cmx - 28cmx + 2x² = 108cm².
Rearranging and simplifying the equation, we have:
2x² - 45cmx + 130cm² = 0.
Now, we can solve this quadratic equation to find the value of 'x' using factoring, completing the square, or the quadratic formula.
Once we find the value of 'x', we will know the width of the strips that were cut off from the cardboard.