Determine whether the triangle, the lengths of whose sides are 2.1 cm, 2.8 cm and 3.5 cm is a right-angled triangle.
Answers
Answer:
Using the Converse of Pythagoras theorem we can conclude that, Triangle formed with the sides 2.1 cm, 2.8 cm and 3.5 cm is a Right-angled triangle.
Question
Determine whether the triangle, the lengths of whose sides are 2.1 cm, 2.8 cm and 3.5 cm is a right-angled triangle.
Given:-
Sides of a triangle are: 2.1 cm, 2.8 cm and 3.5 cm
To find:-
Determining whether the triangle with sides 2.1 cm, 2.8 cm and 3.5 cm will form a right-angled triangle.
Knowledge required:-
Converse of Pythagoras theorem
This theorem states that, If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right-angled triangle.
For a triangle with lengths of sides., AB, BC and AC where AB is the longest side. If
AB² = AC² + BC²
Then By the converse of Pythagoras theorem
Triangle ABC would be a right-angled triangle., right-angled at C.
Solution:-
Given three lengths are:
2.1 cm, 2.8 cm and 3.5 cm
Here, the longest side is AB = 3.5 cm
and the other two sides are BC = 2.1 cm and AC = 2.8 cm
So,
→ AB² = ( 3.5 cm )² = 12.25 cm²
and
→ BC² + AC² = ( 2.1 cm )² + ( 2.8 cm )²
→ BC² + AC² = 4.41 cm² + 7.84 cm²
→ BC² + AC² = 12.25 cm²
Now we can clearly see that,
AB² = BC² + AC²
Hence.,
Using the Converse of Pythagoras theorem we can conclude that,
Triangle formed with the sides 2.1 cm, 2.8 cm and 3.5 cm is a Right-angled triangle.