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 removed.
(17-w)(14-w) = 108
238 - 31w + w^2 = 108
w^2 - 31w + 130
(w-5)(w-26) = 0
w = 5 or 26
w=5, due to the size conditions.
12*9 = 108
12 * 9=108
A piece of cardboard measures 12 cm by 30 cm what is its area in square measure
Baliw ba ako
Well, this is a puzzling situation. So, let me do some calculations while amusing you with a little joke.
Why did the scarecrow win an award? Because he was outstanding in his field!
Now, let's solve this rectangular riddle. We know that the initial area of the cardboard is 17cm by 14cm, which gives us 238cm². After we cut off the strips, the remaining area becomes 108cm².
Let's assume the width of the strips removed is 'w' cm. So, the new dimensions of the cardboard will be (17-w) cm by (14-w) cm. And the area of the remaining piece is:
(17 - w) cm * (14 - w) cm = 108cm²
Expanding this equation, we get:
238 - 31w + w² = 108
Rearranging the terms, we have:
w² - 31w + 130 = 0
Now, we can solve this quadratic equation to find 'w'. Using either factoring or the quadratic formula:
(w - 10)(w - 13) = 0
So, we have two possible widths for the strips: w = 10cm or w = 13cm.
Voilà! The width of the strips removed could be either 10cm or 13cm. I hope you found both the answer and the joke amusing!
To find the width of the strips removed, we can start by visualizing the given situation.
We have a rectangular piece of cardboard measuring 17cm by 14cm. Strips of equal width (let's call it "w") are cut off one side and one end. The remaining piece of cardboard has an area of 108cm^2.
Now, let's calculate the area of the remaining piece after the strips are cut off:
- The original area of the cardboard can be found by multiplying its dimensions: 17cm * 14cm = 238cm^2.
- The area of the remaining piece is given as 108cm^2.
To find the width of the strips removed, we need to subtract the area of the remaining piece from the original area:
238cm^2 - 108cm^2 = 130cm^2.
Since the strips are rectangular and similar in width, we can divide the difference in areas (130cm^2) by the width of each strip to find the number of strips:
130cm^2 / w = number of strips.
Now we can proceed to find the width of the strips by solving the equation:
130cm^2 / w = number of strips.
However, we are missing the value of the number of strips. Unfortunately, the problem does not provide this information. Without knowing the number of strips, we cannot calculate the exact width.