Question

Which of the following forms a right angle triangle
(a) 12 , 8 , 3 (b) 8,7,12 (c) 8,15,17 (d) 5,4,9

Answer 1

the answer is c as
${8}^{2} + {15}^{2} = 64 + 225 = 289 = {17}^{2}$
now as sum of square of two sides is equal to the square of the third side. so by converse of Pythagoras theorem these are the sides of a right angled triangle.

Answer 2

$\huge\textbf{Solution}$

$<b><i>$As we know a right triangle is formed when the sum of square of its height and base is equal to the square of its hypotenuse

So

in option A) 12,8,3

Lets consider that 12 is the longest side so it's a hypotenuse

base = 3 cm and height = 8 cm

h² = p² + b²

(12)² = (8)² +( 3)²

LHS = (12)² = 144

RHS = (8)² +( 3)² = 64 + 9 = 73.

Since LHS ≠ RHS

so it's not a right angled triangle

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In option B ) 8,7,12

Lets consider that 12 is the longest side so it's a hypotenuse

base = 7 cm and height = 8 cm

h² = p² + b²

(12)² = (8)² +( 7)²

LHS = (12)² = 144

RHS = (8)² +( 7)² = 64 + 49 = 113

Since LHS ≠ RHS

so it's not a right angled triangle

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In option c)8,15,17

Lets consider that 17 is the longest side so it's a hypotenuse

base = 8 cm and height = 15 cm

h² = p² + b²

(17)² = (15)² +(8)²

LHS = (17)² = 289

RHS = (15)² +(8)² = 225 + 64 = 289

Since LHS = RHS

so its a right angled triangle
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In option d). 5,4,9

Lets consider that 9 is the longest side so it's a hypotenuse.

base = 4 cm and height = 5 cm

h² = p² + b²

(9)² = (5)² +(4)²

LHS = (9)² = 81

RHS = (5)² +(4)² = 25 + 16 = 41

Since LHS ≠ RHS

so it's not a right angled triangle
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So from the above solution it is clear that option c) is the correct answer

Thanks

Have a colossal day ahead

Be Brainly