हिंदी

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? (A) 15 (B) 13 (C) 5 (D) 12

Advertisements
Advertisements

प्रश्न

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?

विकल्प

  • 15

  • 13

  • 5

  • 12

MCQ
Advertisements

उत्तर

13

Explanation:


In ∆PQR,

∠Q = 90°

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

∴ PR2 = 169   ...[Given]

∴ PR = `sqrt(169)`

Taking square root both the sides,

∴ PR = 13

shaalaa.com
Converse of Pythagoras Theorem
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Pythagoras Theorem - Exercise

संबंधित प्रश्न

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


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


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

30, 40, 50


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 __________


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


If the length of diagonal of square is `sqrt(2)`, then what is the length of each side?


In ∆ABC, AB = `6sqrt(3)` cm, AC = 12 cm, and BC = 6 cm then m∠A = ?


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 ΔABC, AB = 9 cm, BC = 40 cm, AC = 41 cm. State whether ΔABC is a right-angled triangle or not. Write reason.


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×