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
(a) Fill in the length of the third side in each case in the table below.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
For Diagram A with x=4:
The perimeter of the triangle is given as 26 cm. The equation can be set up as:
10+4+L=26L=26−10−4=12extcm
Thus, Length of third side = 12 cm.
For Diagram B with x=9:
10+9+L=26L=26−10−9=7extcm
Therefore, Length of third side = 7 cm.
Step 2
(b) Find the three values of x that make the triangle an isosceles triangle.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To form an isosceles triangle, two sides must be equal. The possible values for x can be found by setting:
10=x
x=10
4+L=10, leading to the third value of x.
Thus the possible values of x are:
x = 10 cm, x = 8 cm, or x = 6 cm.
Step 3
(c)(i) Use the point A on the graph to estimate the area of the triangle in Diagram A.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Based on the graph, the area at point A (where x=4) corresponds to an estimated value of 18 cm².
Step 4
(c)(ii) Plot the point B on the graph to represent the triangle in Diagram B.
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Point B should be plotted at the x-value that corresponds to a length of 7 cm when x = 9, and labeled accordingly on the graph.
Step 5
(c)(iii) Write down the equation of the axis of symmetry.
97%
117 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The axis of symmetry can be observed visually on the graph. From symmetry properties, it would be approximately at:
Equation: x=8.
Step 6
(d) Show that this is not a right-angled triangle.
97%
121 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Using Pythagoras' theorem:
For sides 10, 5, and 11: We check if:
100 + 25 = 121 ext{ (True)}$$
This triangle does not satisfy the condition of Pythagorean theorem for any combination, hence it is not a right-angled triangle.
Step 7
(e) Work out the area of this triangle.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
For x=8cm, we calculate the area:
Using the formula for the area of a triangle:
