English
Maharashtra State BoardSSC (English Medium) 10th Standard

If length of sides of a triangle are a, b, c and a^2 + b^2 = c^2, then which type of triangle it is? (A) Obtuse angled triangle (B) Acute angled triangle (C) Equilateral triangle

Advertisements
Advertisements

Question

If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?

Options

  • Obtuse angled triangle

  • Acute angled triangle

  • Equilateral triangle

  • Right angled triangle

MCQ
Advertisements

Solution

Right angled triangle

Explanation:

If the sides satisfy (a2 + b2 = c2), then by the Pythagorean theorem and its converse the triangle has a 90° angle, with (c) as the hypotenuse.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Pythagoras Theorem - Exercise

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is ______.


From a point O in the interior of a ∆ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove
that :

`(i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2`

`(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2`


Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 50 cm, 80 cm, 100 cm

 


Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals


A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.


 
 

In an equilateral triangle ABC, D is a point on side BC such that BD = `1/3BC` . Prove that 9 AD2 = 7 AB2

 
 

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.


Identify, with reason, if the following is a Pythagorean triplet.

(5, 12, 13)


In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.


In triangle ABC, angle A = 90o, CA = AB and D is the point on AB produced.
Prove that DC2 - BD2 = 2AB.AD.


Find the length of diagonal of the square whose side is 8 cm.


Prove that (1 + cot A - cosec A ) (1 + tan A + sec A) = 2


The sides of a certain triangle is given below. Find, which of them is right-triangle

16 cm, 20 cm, and 12 cm


Use the information given in the figure to find the length AD.


The sides of the triangle are given below. Find out which one is the right-angled triangle?

11, 12, 15


In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD2 = 7 AB2.


In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9BP2 = 9BC2 + 4AC2


In the given figure. PQ = PS, P =R = 90°. RS = 20 cm and QR = 21 cm. Find the length of PQ correct to two decimal places.


Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?


Find the unknown side in the following triangles


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×