4.1:
To determine whether the given triangle is right-angled, acute-angled, or obtuse-angled, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the longest side.
In this case, the three side lengths are 11, 21, and 25. Let's find which side is the longest:
11^2 = 121
21^2 = 441
25^2 = 625
Since 625 is the largest square, it corresponds to the longest side of the triangle, which is 25. Now let's check if this triangle is right-angled:
11^2 + 21^2 = 121 + 441 = 562
We can see that 562 is not equal to 625, so this triangle is not right-angled. Since the sum of the squares of the two shorter sides is less than the square of the longest side, this triangle is obtuse-angled.
4.2:
Once again, we can use the Pythagorean theorem to determine the type of triangle. The side lengths in this case are 4√2, 3√2, and 5√2. We need to find which side is the longest by squaring each side length:
(4√2)^2 = 32
(3√2)^2 = 18
(5√2)^2 = 50
Since 50 is the largest square, it corresponds to the longest side of the triangle, which is 5√2. Now let's check if this triangle is right-angled:
(4√2)^2 + (3√2)^2 = 32 + 18 = 50
We can see that 50 is equal to 50, so this triangle is right-angled.
4.3:
For this triangle with side lengths 8, 10, and 2, let's determine the type using the Pythagorean theorem. Squaring each side length gives:
8^2 = 64
10^2 = 100
2^2 = 4
The largest square is 100, corresponding to the longest side length of 10. Now let's check if this triangle is right-angled:
8^2 + 2^2 = 64 + 4 = 68
We can see that 68 is not equal to 100, so this triangle is not right-angled. Since the sum of the squares of the two shorter sides is less than the square of the longest side, this triangle is obtuse-angled.
4. the side lengths of different triangles are given determine whether they are right-angled, acute -angled or obtuse-angled
4.1 11; 21; 25
4.2 4√2; 3√2; 5√2
4.3 8; 10; 2
1 answer
1 answer