हिंदी

Sides of the Triangle Are 7 Cm, 24 Cm, and 25 Cm. Determine Whether the Triangle is a Right-angled Triangle Or Not. - Geometry Mathematics 2

Advertisements
Advertisements

प्रश्न

Sides of the triangle are 7 cm, 24 cm, and 25 cm. Determine whether the triangle is a right-angled triangle or not. 

योग
Advertisements

उत्तर

The longest side is 25 cm. 

∴ (25)2 = 625                                                          ....(i)

  Now, sum of the squares of the other two sides will be 

(7)2 + (24)2 = 49 + 576

                   = 625                                                   ....(ii)

∴ (25)2 = (7)2 + (24)2                                                  .....[ From (i) and (ii)]

Yes, the given sides form a right angled triangle .  ......[By converse of pythagoras theorem]

shaalaa.com
Converse of Pythagoras Theorem
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2013-2014 (October)

APPEARS IN

संबंधित प्रश्न

In the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle?


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.


If in ∆ABC, DE || BC. AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is


In a ∆ABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is


8, 15, 17 is a Pythagorean triplet


The incentre is equidistant from all the vertices of a triangle


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

8, 15, 17


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

12, 13, 15


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

30, 40, 50


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

9, 40, 41


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

24, 45, 51


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?


Choose the correct alternative:

A rectangle having length of a side is 12 and length of diagonal is 20, then what is length of other side?


If a triangle having sides 50 cm, 14 cm and 48 cm, then state whether given triangle is right angled triangle or not


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×