Question

if the sides of a triangle are 1.2 cm and 3.5 cm and 3.7 cm is this triangle a right angle triangle if so which side is a hypotenuse​

Answer 1

Step-by-step explanation:

3.7 is hypotenuse in the triangle

Answer 2

Yes, it is a right angled triangle with hypotenuse equal to 3.7 cm.

Step-by-step explanation:

Given:

The sides of the triangle are 1.2 cm, 3.5 cm and 3.7 cm.

Let the vertices be A, B, and C and let AB = 1.2 cm, BC = 3.5 cm and AC = 3.7 cm.

Now, if the given triangle ABC has to be a right angled triangle, then, by Pythagoras theorem, sum of the squares of its legs must be equal to the square of its hypotenuse.

The hypotenuse is the largest side of the right angled triangle. Here, the side AC is the largest side as $3.7>3.5>1.2$.

Now, the legs of the triangle are the other two sides which are AB and BC.

Now, let us first find the sum of the squares of its legs.

$AB^2+BC^2=1.2^2+3.5^2=1.44+12.25=13.69\\AB^2+BC^2=13.69---1$

Now, the square of the side AC is:

$AC^2=3.7^2\\AC=13.69----2$

Now, from equations (1) and (2), we conclude that:

$AB^2 + BC^2 = AC^2$

Since, it follows Pythagoras theorem, the triangle is a right angled triangle with the side having length 3.7 cm as the hypotenuse.