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Monica has a set of nine coloured plastic strips (long red, middle red, short red, etc.) as shown below - Junior Cycle Mathematics - Question 8 - 2014
Question 8
Monica has a set of nine coloured plastic strips (long red, middle red, short red, etc.) as shown below. The strips can be joined together, to form geometrical objec... show full transcript
Worked Solution & Example Answer:Monica has a set of nine coloured plastic strips (long red, middle red, short red, etc.) as shown below - Junior Cycle Mathematics - Question 8 - 2014
Step 1
i) Is it possible to make an object in the shape of an isosceles triangle using any three of the nine strips? Give a reason for your answer.
Answer
No, it is not possible to form an isosceles triangle. An isosceles triangle requires two sides of equal length. In the given strips, none of the strips are of equal length; therefore, constructing an isosceles triangle is impossible.
Step 2
ii) Monica would like to join four strips together to form an object in the shape of a parallelogram. Explain why it is not possible to do this.
Answer
In a parallelogram, opposite sides must be equal in length. However, given the strips, there are no pairs of strips that have the same length, making it impossible to select four strips that can create a parallelogram.
Step 3
iii) The long yellow, long blue and short red strips are used to form an object in the shape of a triangle. Monica thinks that this might be a right-angled triangle. Investigate if she is correct.
Answer
To check if the triangle formed by the strips is a right-angled triangle, we can apply the Pythagorean theorem. The lengths of the strips are as follows: yellow = 25 cm, blue = 24 cm, and short red = 7 cm. We verify whether:
Where is the longest side (25 cm) and and are the other two sides (24 cm and 7 cm).
Calculating:
625 = 576 + 49\ 625 = 625$$ This confirms that the triangle is a right-angled triangle.Step 4
iv) Monica uses the long blue and the long white strips to form the arms of a right angle. Find the length of a strip that would be needed to complete this triangular shape. Give your answer correct to two decimal places.
Answer
The long blue strip is 24 cm and the long white strip is 20 cm. To find the length of the strip that would connect the ends of these strips (the hypotenuse), we apply the Pythagorean theorem:
\text{Let } c = \text{ hypotenuse (length we seek)}\ a = 24\ b = 20\ \Rightarrow c^2 = 24^2 + 20^2 = 576 + 400 = 976\ \Rightarrow c = \sqrt{976} ≈ 31.24\Thus, the length of the strip required to complete the triangle is approximately 31.24 cm.