Advertisements
Advertisements
प्रश्न
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 12, 15
Advertisements
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, 12, and 15.
Let us check whether the given set (11, 12, 15) forms a Pythagorean triplet or not.
The biggest number among the given set is 15.
(15)2 = 225; (11)2 = 121; (12)2 = 144
Now, 121 + 144 = 265 ≠ 225
∴ (11)2 + (12)2 ≠ (15)2
Thus, (11, 12, 15) does not form a Pythagorean triplet.
Hence, the given triangle with sides 8, 15, and 17 is not a right-angled triangle.
संबंधित प्रश्न
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90o. Calculate the length of AB.
In the figure below, find the value of 'x'.
Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.
Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.
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: 9AQ2 = 9AC2 + 4BC2
∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.
There are two paths that one can choose to go from Sarah’s house to James's house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street?
The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then AB equals ______.
Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.
