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प्रश्न
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 60, 61
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उत्तर
It is known that, if in a triplet of natural numbers, the square of the biggest number is equal to the sum of the squares of the other two numbers, then the three numbers form a Pythagorean triplet. If the lengths of the sides of a triangle form such a triplet, then the triangle is a right-angled triangle.
The sides of the given triangle are 11, 60, and 61.
Let us check whether the given set (11, 60, 61) forms a Pythagorean triplet or not.
The biggest number among the given set is 61.
(61)2 = 3721; (11)2 = 121; (60)2 = 3600
Now, 121 + 3600 = 3721
∴ (11)2 + (60)2 = (61)2
Thus, (11, 60, 61) forms a Pythagorean triplet.
Hence, the given triangle with sides 11, 60, and 61 is a right-angled triangle.
संबंधित प्रश्न
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
(A) 4
(B) 3
(C) 2
(D) 1
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`
In an equilateral triangle ABC, D is a point on side BC such that BD = `1/3BC` . Prove that 9 AD2 = 7 AB2
Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)
In ∆ ABC, AD ⊥ BC.
Prove that AC2 = AB2 +BC2 − 2BC x BD
Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm
Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.
In the figure, find AR
If S is a point on side PQ of a ΔPQR such that PS = QS = RS, then ______.
Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.
