मराठी
महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

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? - Geometry Mathematics 2

Advertisements
Advertisements

प्रश्न

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?

पर्याय

  • 15

  • 13

  • 5

  • 12

MCQ

उत्तर

13

In ∆PQR,

∠Q = 90°

∴ PR2 = PQ2 + QR2    ...[Pythagoras theorem]

∴ PR2 = 169               ...[Given]

∴ PR = `sqrt(169)`

Taking square root both the sides,

∴ PR = 13

shaalaa.com
Converse of Pythagoras Theorem
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Pythagoras Theorem - Q.1 (A)

संबंधित प्रश्‍न

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


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


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 


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


Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?


8, 15, 17 is a Pythagorean triplet


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


The area of a rectangle of length 21 cm and diagonal 29 cm is __________


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


If a triangle having sides 8 cm, 15 cm and 17 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).


In a right angled triangle, right-angled at B, lengths of sides AB and AC are 5 cm and 13 cm, respectively. What will be the length of side BC?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×