Miki has a sheet of paper with a length of 104 centimeters and a width of 88 centimeters. She wants to divide it into the larges
t squares possible without wasting any paper. How many squares of the largest size will she be able to cut from the paper? 13 squares, 26 squares, 143 squares, or 572 squares
1 answer:
First, find the area of the rectangular paper: 104 × 88 = 9152 cm²
Since we want to find the number of the largest square that we can cut from the paper, we need to investigate if there's any square number is the factor of 9152
We can use the prime factor tree to find the factors of 9152 that is also a square number as shown below
9152 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 13
after trying few combinations, we have:
2 × 2 × 2 × 2 = 16
2 × 2 × 2 × 2 × 2 × 2 = 64
The largest square number is 64, and we will have 9152 ÷ 64 = 143 squares of papers
Since we want to find the number of the largest square that we can cut from the paper, we need to investigate if there's any square number is the factor of 9152
We can use the prime factor tree to find the factors of 9152 that is also a square number as shown below
9152 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 13
after trying few combinations, we have:
2 × 2 × 2 × 2 = 16
2 × 2 × 2 × 2 × 2 × 2 = 64
The largest square number is 64, and we will have 9152 ÷ 64 = 143 squares of papers
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1 - The equation is:
Since it has no variable on exponents and it has a term with x to the second power, this is a quadratic function.
2 - <em>x</em> represents the length of the tomato patch, so if we want the area of the bell pepper patch, we can input x = 8 into the function:
Thus, the area is 16 square feet.
3 - Since the leading coefficient is negative, the vertex of the parabola gives the maximum value for the function.
The <em>x</em> value of the vertex is:
So, in this case:
And to find the value for the area, we need to input that into the function:
Thus, the maximum area is 18 square feet.
4 - The value for the length of the tomato patch is just the corresponding <em>x</em> for this maximum, which we calculated as the vertex <em>x</em>:
Thus, the length of the tomato patch for this maximum value is 6 feet.