A triangle has one side of length 10 cm and another side of length x cm - Junior Cycle Mathematics - Question 7 - 2019
Question 7
A triangle has one side of length 10 cm and another side of length x cm.
The perimeter of this triangle is 26 cm in length.
(a) Fill in the length of the third side... show full transcript
Worked Solution & Example Answer:A triangle has one side of length 10 cm and another side of length x cm - Junior Cycle Mathematics - Question 7 - 2019
Step 1
Fill in the length of the third side for Diagram A
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Answer
In Diagram A, the perimeter of the triangle is given as 26 cm. One side is 10 cm, and the other side is x cm, where x = 4 cm. Therefore, the length of the third side can be calculated as follows:
Fill in the length of the third side for Diagram B
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Answer
In Diagram B, where x = 9 cm, the calculation for the length of the third side is:
extLengthofthirdside=26−10−9=7extcm.
Step 3
Find the three values of x that make the triangle an isosceles triangle
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Answer
To form an isosceles triangle, two sides must be equal. The possible values for x that satisfy this condition are:
If x = 10 cm, then the other two sides will be equal to 10 cm each.
If x = 10 cm, then both lengths can equal 10 cm and the third side becomes 6 cm.
If x = 6 cm, then two sides can be 10 cm, resulting in another isosceles configuration.
Thus, the values are:
x = 10 cm, x = 6 cm, or x = 10 cm.
Step 4
Estimate the area of the triangle in Diagram A
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Answer
For the triangle with x = 4 cm, we can apply the base-height formula to find the area. By observing point A on the graph, the estimated area appears to be around 18 cm².
Step 5
Plot point B to represent Diagram B
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Answer
On the same graph, plot point B corresponding to x = 9 cm. The area for this configuration should be calculated and labeled accordingly.
Step 6
Equation of the axis of symmetry
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Answer
Given the symmetry of the graph, the equation of the axis of symmetry can be identified with:
x=8.
Step 7
Show that the triangle with sides 10 cm, 5 cm, and 11 cm is not right-angled
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Answer
To show that this triangle is not right-angled, we can apply the Pythagorean theorem. Checking:
102+52=100+25=125eq121=112.
Since the equality does not hold, this triangle is not right-angled.
Step 8
Work out the area of the triangle with biggest area
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Answer
For a triangle with sides of 10 cm, base of 8 cm, and height corresponding to x = 8 cm, we can take half the base multiplied by height (from the graph):
