Question

The hypotenuse of a right triangle is 34cm. find the length of the two legs, if one leg is 14cm longer than the other.

Answer 1

The rule of Pythagoras:

c ^ 2 = a ^ 12 + b ^ 2

In this case :


c = 34 cm

b = a + 14


c = a ^ 2 + ( a + 14 ) ^ 2

34 ^ 2 = a ^ 2 + ( a + 14 ) ^ 2

1156 = a ^ 2 + a ^ 2 + 2 * a * 14 + 14 ^ 2

1156 = 2 a ^ 2 + 28 a + 196 Subtract 196 to both sides

1156 - 196 = 2 a ^ 2 + 28 a + 196 - 196

960 = 2 a ^ 2 + 28 a Divide both sides by 2

480 = a ^ 2 + 14 a Add 49 to both sides

480 + 49 = a ^ 2 + 14 a + 49

529 = ( a + 7 ) ^ 2

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Becouse :

( a + 7 ) ^ 2 = a ^ 2 + 2 * a * 7 + 7 ^ 2 =

a ^ 2 + 14 a + 49

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sqrt ( 529 ) = sqrt [ ( a + 7 ) ^ 2 ]

+ OR - 23 = a + 7


1 case:

23 = a + 7 Subtract 7 to both sides

23 - 7 = a + 7 - 7

16 = a

a = 16 cm


2 case:

- 23 = a + 7 Subtract 7 to both sides

- 23 - 7 = a + 7 - 7

- 30 = a

a = - 30 cm

Length can't be negative so:

a = 16 cm

b = a + 14 = 16 + 14 = 30 cm