High School

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1. Mr. Koloi needs to measure a length of 17cm. He has three sticks of lengths 10cm, 12cm, and 13cm. How can he use all three sticks to measure a length of 17cm?

2. A side of Square B is four times the length of a side of Square A. How many times greater is the area of Square B than the area of Square A?

Answer :

To solve these two questions, let's break them down one by one:

  1. Measuring a Length of 17 cm with Sticks:

    Mr. Koloi has three sticks: 10 cm, 12 cm, and 13 cm. To measure a length of 17 cm using these sticks, we can use a combination of these sticks such that the difference between two of the stick lengths equals 17 cm:

    • If Mr. Koloi places the 10 cm stick alongside the 13 cm stick, he creates a length of 23 cm.

    • By subtracting the 6 cm length of the 12 cm stick, which can be imagined as acting like a 'gap' or subtraction of length upon placing/staggering), he can achieve 17 cm:

      [tex]23 \text{ cm (10 cm + 13 cm)} - 6 \text{ cm (12 cm)} = 17 \text{ cm}[/tex]

    This approach uses all three sticks to measure the required length of 17 cm.

  2. Comparing Areas of Square A and Square B:

    Let's assume the side length of Square A is [tex]s[/tex] cm. Therefore, the side length of Square B, which is four times that of Square A, is [tex]4s[/tex] cm.

    The area of Square A is calculated as:

    [tex]\text{Area of Square A} = s^2[/tex]

    The area of Square B is:

    [tex]\text{Area of Square B} = (4s)^2 = 16s^2[/tex]

    To find how many times greater the area of Square B is compared to the area of Square A, we divide the area of Square B by the area of Square A:

    [tex]\text{Factor of Increase} = \frac{16s^2}{s^2} = 16[/tex]

    Therefore, the area of Square B is 16 times greater than the area of Square A.

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Rewritten by : Barada