The hypotenuse of a right angled triangle is 17 cm long and difference between the other two sides is 7 cm. Find the lengths of the two unknown sides.
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Let one side be x.
Then other side is x+7
x²+(x+7)²=289 Pythagoras Theorem
x²+x²+14x+49=289
2x²+14x-240=0
x²+7x-120=0
(x+15)(x-8)=0
x=-15 or 8
Length cannot be -ve
so x=8
Length of one side =8cm
Length of other side=15cm
Then other side is x+7
x²+(x+7)²=289 Pythagoras Theorem
x²+x²+14x+49=289
2x²+14x-240=0
x²+7x-120=0
(x+15)(x-8)=0
x=-15 or 8
Length cannot be -ve
so x=8
Length of one side =8cm
Length of other side=15cm
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