Question

Will sides 3cm, 5cm,7cm form a right triangle? Justify your answer

Answer 1

Answer:

No

Step-by-step explanation:

The relation between the sides of any right - angled triangle is well given by Pythagoras and this theorem is known as Pythagoras theorem.

In a right angled triangle,

Hypotenuse is the longest side and is denoted by h.

h = 7 cm

Now perpendicular and base can be any of the two measurements and are denoted by p and b respectively.

p = 3 cm

b = 5 cm

By Pythagoras theorem,

h² = p² + b²

Now, if this relation is satisfied by the given measurements, these measurements will form a right - angled triangle. So let us begin by substituting the values,

LHS,

7²

49 cm²

RHS,

3² + 5²

9 + 25 = 34 cm²

Now,

49 ≠ 34

Hence,

These measurements cannot form a right - angled triangle.

Answer 2

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▶ Question - Will sides 3 cm, 5 cm and 7 cm form a right triangle ? Justify your answer.



▶ Explanation :-



In order to form a triangle sum of the sum of two sides should be greater than the third side



=> 3 + 5 = 8


8 > 7



=> 7 + 5 = 12

12 > 3


=> 7 + 3 = 10

10 > 12


∴ Given measurements form a triangle


But to form a right angled triangle, the square of the larger side should be equal to the square of other sides.


=> 7^2 = 49


=> 5^2 + 3^2 = 25 + 9


=> 5^2 + 3^2 = 34


34 ≠ 49


∴ Given measurements do not form a right angled triangle




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