Question

2) एका त्रिकोणाच्या बाजूची लांबी अनुक्रमे 11 सेमी. 60 सेमी 361 सेमी आहे. तर हा
त्रिकोण काटकोन त्रिकोण आहे का?​

Answer 1

Given:

एका त्रिकोणाच्या बाजूची लांबी अनुक्रमे 11 सेमी. 60 सेमी 61 सेमी आहे.

If the length of the sides of the triangle are 11 cm 60 cm and 61 cm respectively

To find:

तर हा त्रिकोण काटकोन त्रिकोण आहे का?​

State with reason whether the triangle is a right angle triangle or not​?

Solution:

Pythagorean Theorem: This theorem states that the sum of squares of the two short sides of a right-angled triangle is equal to the square of the hypotenuse.

The Pythagorean Theorem consists of the following formula:

$\boxed{\bold{c^2 = a^2 + b^2}}$

where a = side of a right-angled triangle, b = side of a right-angled triangle and c = hypotenuse

Here we have the three sides of the triangle as

a = 11 cm

b = 60 cm

c = 61 cm

The sum of squares of the two short sides of the given triangle is,

= a² + b²

= 11² + 60²

= 121 + 3600

= 3721 . . .  Equation 1

The square of the third side of the given triangle is,

= c²

= 61²

= 3721 . . . . Equation 2

Therefore, from equation 1 and equation 2, we get

3721 = 3721

⇒ c² = a² + b²

⇒ The given triangle satisfies the Pythagorean Theorem

Thus,  The triangle is a right-angled triangle.

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