The lengths of the sides of some triangles are given below. Find the right-angled triangles among these.
(i) 7 centimeters, 15 centimeters, 17 centimeters
(ii) 8 centimeters, 24 centimeters, 25 centimeters
(iii) 6 centimeters, 8 centimeters, 10 centimeters
(iv) 1.5 centimeters, 1.6 centimeters, 2.5 centimeters
The lengths of the sides of some triangles are given below. Find the right-angled triangles among these.
(i) 7 centimeters, 15 centimeters, 17 centimeters
(ii) 8 centimeters, 24 centimeters, 25 centimeters
(iii) 6 centimeters, 8 centimeters, 10 centimeters
(iv) 1.5 centimeters, 1.6 centimeters, 2.5 centimeters
(i)The given sides of the triangle are 7 cm, 15 cm and 17 cm.
Square of the longest side = (17 cm)2 = 289 cm2
Sum of the squares of the other two sides = (7 cm)2 + (15 cm)2
= (49 + 225) cm2
= 274 cm2
Since the square of the longest side is not equal to the sum of the squares of the other two sides, the given sides are not the sides of a right-angled triangle.
(ii) The given sides of the triangle are 8 cm, 24 cm and 25 cm.
Square of the longest side = (25 cm)2 = 625 cm2
Sum of the squares of the other two sides = (8 cm)2 + (24 cm)2
= (64 + 576) cm2
= 640 cm2
Since the square of the longest side is not equal to the sum of the squares of the other two sides, the given sides are not the sides of a right-angled triangle.
(iii) The given sides of the triangle are 6 cm, 8 cm and 10 cm.
Square of the longest side = (10 cm)2 = 100 cm2
Sum of the squares of the other two sides = (6 cm)2 + (8 cm)2
= (36 + 64) cm2
= 100 cm2
Since the square of the longest side is equal to the sum of the squares of the other two sides, the given sides are the sides of a right-angled triangle.
(iv) The given sides of the triangle are 1.5 cm, 1.6 cm and 2.5 cm.
Square of the longest side = (2.5 cm)2 = 6.25 cm2
Sum of the squares of the other two sides = (1.5 cm)2 + (1.6 cm)2
= (2.25 + 2.56) cm2
= 4.81 cm2
Since the square of the longest side is not equal to the sum of the squares of the other two sides, the given sides are not the sides of a right-angled triangle.
(i)The given sides of the triangle are 7 cm, 15 cm and 17 cm.
Square of the longest side = (17 cm)2 = 289 cm2
Sum of the squares of the other two sides = (7 cm)2 + (15 cm)2
= (49 + 225) cm2
= 274 cm2
Since the square of the longest side is not equal to the sum of the squares of the other two sides, the given sides are not the sides of a right-angled triangle.
(ii) The given sides of the triangle are 8 cm, 24 cm and 25 cm.
Square of the longest side = (25 cm)2 = 625 cm2
Sum of the squares of the other two sides = (8 cm)2 + (24 cm)2
= (64 + 576) cm2
= 640 cm2
Since the square of the longest side is not equal to the sum of the squares of the other two sides, the given sides are not the sides of a right-angled triangle.
(iii) The given sides of the triangle are 6 cm, 8 cm and 10 cm.
Square of the longest side = (10 cm)2 = 100 cm2
Sum of the squares of the other two sides = (6 cm)2 + (8 cm)2
= (36 + 64) cm2
= 100 cm2
Since the square of the longest side is equal to the sum of the squares of the other two sides, the given sides are the sides of a right-angled triangle.
(iv) The given sides of the triangle are 1.5 cm, 1.6 cm and 2.5 cm.
Square of the longest side = (2.5 cm)2 = 6.25 cm2
Sum of the squares of the other two sides = (1.5 cm)2 + (1.6 cm)2
= (2.25 + 2.56) cm2
= 4.81 cm2
Since the square of the longest side is not equal to the sum of the squares of the other two sides, the given sides are not the sides of a right-angled triangle.
Perimeter of the triangle = ___ centimeters.
