The two perpendicular sides (legs) of a right triangle, measured in cm, are the zeroes of x² − 17x + 60. Without finding the two legs separately, work out the length of the hypotenuse.

Question

Accepted Answer

13 cm. + = 17 and = 60 . By Pythagoras the hypotenuse is √ ^2 + ^2 , and ^2 + ^2 = ( + )^2 - 2 = 289 - 120 = 169 . So the hypotenuse is √169 = 13 cm. (The legs are 5 cm and 12 cm, and 5^2 + 12^2 = 169 .) 17 cm is the sum of the legs; 169 cm forgets the square root; 12 cm is one of the legs, not the hypotenuse.

The two perpendicular sides (legs) of a right triangle, measured in cm, are the zeroes of $x^{2} - 17 x + 60$ .
Without finding the two legs separately, work out the length of the hypotenuse.

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More Class 10 Zeroes and Coefficients practice

The two perpendicular sides (legs) of a right triangle, measured in cm, are the zeroes of x2−17x+60.Without finding the two legs separately, work out the length of the hypotenuse.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Zeroes and Coefficients practice

The two perpendicular sides (legs) of a right triangle, measured in cm, are the zeroes of $x^{2} - 17 x + 60$ .
Without finding the two legs separately, work out the length of the hypotenuse.