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?

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 - Q.1 (A)

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.


P and Q are the mid-points of the sides CA and CB respectively of a ∆ABC, right angled at C. Prove that:

`(i) 4AQ^2 = 4AC^2 + BC^2`

`(ii) 4BP^2 = 4BC^2 + AC^2`

`(iii) (4AQ^2 + BP^2 ) = 5AB^2`


PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR


Tick the correct answer and justify: In ΔABC, AB = `6sqrt3` cm, AC = 12 cm and BC = 6 cm.

The angle B is:


The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.


In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF


In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.


In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.

Prove that: 2AB= 2AC+ BC2


In an isosceles triangle, length of the congruent sides is 13 cm and its base is 10 cm. Find the distance between the vertex opposite the base and the centroid.


If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.


In a quadrilateral ABCD, ∠B = 90° and ∠D = 90°.
Prove that: 2AC2 - AB2 = BC2 + CD2 + DA2


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

6 m, 9 m, and 13 m


A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.


Find the Pythagorean triplet from among the following set of numbers.

3, 4, 5


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

1.5, 1.6, 1.7


Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.


Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.


In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.


Rithika buys an LED TV which has a 25 inches screen. If its height is 7 inches, how wide is the screen? Her TV cabinet is 20 inches wide. Will the TV fit into the cabinet? Give reason


The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×