English
Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 8

Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem 24, 45, 51 - Mathematics

Advertisements
Advertisements

Question

Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem

24, 45, 51

Sum
Advertisements

Solution

Take a = 24, b = 45 and c = 51

Now a2 + b2 = 242 + 452

= 576 + 2025

= 2601

c2 = 512 = 2601

∴ a2 + b2 = c2

Yes, By the converse of Pyhtagoreas theorem, the triangle with given measure is a right angled triangle.

shaalaa.com
Converse of Pythagoras Theorem
  Is there an error in this question or solution?
Chapter 5: Geometry - Exercise 5.2 [Page 178]

APPEARS IN

Samacheer Kalvi Mathematics [English] Class 8 TN Board
Chapter 5 Geometry
Exercise 5.2 | Q 3. (v) | Page 178

RELATED QUESTIONS

In ∆PQR, PQ = √8 , QR = √5 , PR = √3. Is ∆PQR a right-angled triangle? If yes, which angle is of 90°?


The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle


5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.


In the adjacent figure, ABC is a right angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE2 = 3AC2 + 5AD2 


Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem

9, 40, 41


Choose the correct alternative:

In right angled triangle, if sum of the squares of the sides of right angle is 169, then what is the length of the hypotenuse?


If a triangle having sides 8 cm, 15 cm and 17 cm, then state whether given triangle is right angled triangle or not


A rectangle having dimensions 35 m × 12 m, then what is the length of its diagonal?


In ∆LMN, l = 5, m = 13, n = 12 then complete the activity to show that whether the given triangle is right angled triangle or not.
*(l, m, n are opposite sides of ∠L, ∠M, ∠N respectively)

Activity: In ∆LMN, l = 5, m = 13, n = `square`

∴ l2 = `square`, m2 = 169, n2 = 144.

∴ l2 + n2 = 25 + 144 = `square`

∴ `square` + l2 = m2

∴By Converse of Pythagoras theorem, ∆LMN is right angled triangle.


In the given figure, triangle PQR is right-angled at Q. S is the mid-point of side QR. Prove that QR2 = 4(PS2 – PQ2).


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×