Question

Construct ΔNIB in which NI=5.6 cm, IB=6 cm and BN=6 cm. What type of triangle is this?

Answer 1

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☆It will be Isolesce triangle because two of the sides of triangle are same 6 cm and only one side is different.

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Answer 2

The triangle ΔNIB is a right-angled triangle.

Given, the sides of the triangle are NI=5.6 cm, IB=6 cm and BN=6 cm.

To construct a triangle with these sides, we can use the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

The sum of 5.6 + 6 = 11.6 cm and 6 + 6 = 12 cm, which are both greater than the length of the third side 5.6 cm. So, it is possible to construct a triangle with these side lengths.

Now, let's examine the triangle with respect to its angles.

Given that,

$a^2 + b^2 = c^2$ (Pythagorean theorem)

$5.6^2 + 6^2 = c^2$

$31.36 + 36 = c^2$

$67.36 = c^2$

c = √67.36 = 8.24

Now,

$c^2 > a^2 + b^2$ (Pythagorean theorem)

$8.24^2 > 5.6^2 + 6^2$

67.36 > 31.36 + 36

67.36 > 67

This means that c > a , c > b. So the angle opposite to c (hypotenuse) is greater than the other two angles, thus it is a right-angled triangle.

So, the triangle ΔNIB is a right-angled triangle.

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