Question

Hypotenuse of a right angle triangle is 13 cm and difference between other two side is 7 cm taking x is the length of one of the two sides write an equation X that represents the above statement solve the equation obtained in above and hence find the two unknown sides of triangle

Answer 1

Answer:

$given \: hypotenuse = 13cm \\ \\ let \: one \: side \: = xcm \\ \\ difference \: of \: two \: sides = 7. \\ \\ \\ by \: using \: pythagoreas \: theorem \\ \\ {13}^{2} = {x }^{2} + {12 }^{2} \\ \\ 169 - 144 = x2 \\ \\ \\ x2 = 25 \\ \\ x = 5cm \\ \\ \\ the \: two \: sides \: are \: 5cm \: 12 \: cm$

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Answer 2

Let one of the other sides be x then the other side is x+7.

Then according to the problem,

x

2

+(x+7)

2

=13

2

or, 2x

2

+14x−120=0

or, x

2

+7x−60=0

or, x

2

+12x−5x−60=0

or, (x−5)(x+12)=0

or, x=5. [ Since x



=−12]

So the other sides are 5 cm and 5+7=12 cm.