Question

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 108cm². find the width of the strips removed .

Answer 1

5 cm

Explanation:

The rectangular piece of cardboard is original of measurements 17 cm by 14 cm.

Let the width of the strips is x cm.

So, the new width and length of the cardboard will be (14 - x) cm and (17 - x) cm respectively.

Hence, the area of the new cardboard will be = (14 - x )(17 - x) = 108

⇒ 238 - 31x + x² = 108

⇒ x² - 31x + 130 = 0

⇒ x² - 26x - 5x + 130 = 0

⇒ (x - 26)(x - 5) = 0

⇒ x = 26 or x = 5

Now, x can not be greater than 14 cm.

Therefore, the width of the strips will be 5 cm. (Answer)